Suggestions Needed & Proposal thoughts

Couple of issues / concerns.

I suspect you have not researched much about driving in Italy.
Car will not be your friend in Pisa, Florence, Rome, Venice, Genoa or and likely not in Portofino either.
Cars and Italian cities mix as well as oil and water.
You should lose the car except for the drive from Florence to Rome ; picking the car up leaving Florence and dropping it off before entering any Rome ZTL areas.
I would take Pisa off the list of nights. Stop by and see the tower and neighboring piazza if you like but think the night can be better used as another night while you have the car in Tuscany between Florence and Rome or another night in Florence if you would prefer more.

Take the train from Rome to Venice don't drive that part.

Been everywhere on your list but Portofino/Genoa have been to nearby Cinque Terre

Where to propose is a tough question, I think playing it by ear and trusting your gut on when feels right is the best idea. Wouldn't want to wait until Venice and if something goes out of plan feeling like you have to force a moment.
Maybe the time in Portofino overlooking the sea will be right, maybe at night overlooking the Duomo in Florence, or on the streets of Rome will.
Most everywhere you are going will be romantic so I wouldn't stress about planning that detail and let it happen!

I think you would enjoy your two weeks more if you slowed down as you visit Italy. I suggest you leave Venice to another time OR leave Rome for another trip. My preference would be for Venice over Rome. In early May, all Italy should be nice. May day (May 1) is a major holiday in parts of Europe. People are traveling and especially going to places like Portofino. Wherever you are on that weekend, have hotel reservations set up. I see May 1 is on a Tuesday in 2018, so maybe you could skip it by flying to Milan after the first.

I agree that your itinerary seems a little aggressive, and perhaps exhausting. 8 travel days in 2 weeks!

I would suggest consolidating a bit. See Pisa either on the way to Florence from Portofino, or as a day trip from Florence. Same thing for Tuscany. Stay in Florence and day trip from there.

I also have concerns about your use of a car for the whole trip. I'd think long and hard about having a car for any Italian city. You might want to do a search on this forum on that subject. Trains can be much more hassle free.

And about the proposal - I'd recommend you do it in Portofino, before she gets too fatigued from the trip.

Suggestion about overcoming jet lag: consensus seems to be that it's best to make yourself stay up until bed time in your new time zone, and to spend a lot of the day walking around outdoors. In other words, catching up on sleep during the day just makes it more difficult to adjust.

Thanks for the tips. I'll look into using the train a bit more, but really like the idea of being able to stop along the way. I've researched parking in Rome and Florence and have found public and private structures just outside of these cities.

Also, we'll be arriving late evening on the 17th so hopefully it feels like we're going to bed at a normal time.

Do the trip in reverse order and propose in Venice on an evening gondola ride?

Skip Portofino and do Lake Como at the end.

Pisa is good for a couple hours to the the Tower, but really does not need to be an overnight stop.

thats my $0.02

Viamichelin.com estimates the driving time between Rome and Venice via the fastest route at 6 hours. That does not include any stops, getting lost, the impact of traffic, or navigational errors. The consensus on the forum is that viamichelin.com is optimistic. So I really question whether you'll have time to stop anywhere that day except to get some lunch.

By comparison, the train takes 3 hours 45 minutes, and you can pack a lunch and eat on the way if you want to save time.

Not yet mentioned in this thread is the number of people who have returned from lovely Italian vacations and--months later--received very costly Italian traffic tickets. That won't happen if you take the train. Taking the train also avoids the thorny question of how you'll deal with your luggage when you stop along the way to your new hotel. Theft from unattended vehicles is a problem at tourist sites.

My son-in-law proposed to my daughter on the shores of Lake Garda. He was successful. I suppose Lake Como might do just as well.

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but really like the idea of being able to stop along the way. I've researched parking in Rome and Florence and have found public and private structures just outside of these cities.

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You may have researched where to park but have you read up on ZTL zones in every single city including some places you might casually stop by on your way? Smaller cities the ancient walls signal you to not drive in as long as you know of the ZTL's existence but in the larger cities there can be multiple ZTL zones outside of the city walls/gates.

Also, with your fast moving plan you have no time to be parking far outside each city and then needing transportation to get to your lodging each night ; that would take far too long with your fast passed schedule.
Your schedule as others have commented is fast paced, if you want to have it also be romantic there is no time for leisurely driving with stopping, you need to get from point A to point B to stay on your schedule.

Keeping a car while in Rome or Florence is a waste of resources and a hassle. It is hard to get over the American desire for control that includes a "must have a car" attitude, but it insulates you from the real European experience in the cities.

Rent one for Tuscany, yes, but driving across Italy (between Venezia and Roma) and parking it while in cities is not an intelligent decision.

Also, skip Pisa and SLOW DOWN. Sleep in three-four locations maximum in your time there. Have a trip to remember.

Since you asked for advice....

[N.B. I lived in Roma for years and only drive OUT of town. Parking is awful and expensive.]

I agree with the others. Slow your trip down. It will be more enjoyable that way.

I wouldn't drive in Italy unless I had to (ZTLs, parking, electronic speed enforcement). No thanks.

In case you feel like proposing in Rome, this recent post may offer some options.

https://community.ricksteves.com/travel-forum/italy/rome-rooftop-bars-restaurants

If only someone had proposed to me somewhere on the edge of Lake Como..... ;)

Propose early so you can both relax and you (hopefully) don't have to worry where the ring is! Make sure your future life partner is in a good mood, rested, and comfortable (ie, not sick).

Lake Como is heaven on earth. Varenna on Lake Como is not far from Milan by train and is a perfect place to unwind and a PERFECT place to propose! You'll fully understand why George Clooney has a house there!

Check out the romantic Hotel Villa Cipressi with its own garden on the banks of the lake.

That ring will be burning a hole in your pocket and Lake Como will afford many private romantic moments for your proposal. You can stroll along the banks on the walking path in Varenna, cruise around on the ferry, and get lost in gardens at the Villa Carlotta. But maybe you'll find that perfect moment in the classic terrace gardens of the Villa Balbianello...

You can go be touristas from there!

Genoa is not a common jumping-off point for newcomers to Italy. What draws you there?

Did you know you can get from Varenna to Florence and Pisa easily by train?

If you get to Florence and still haven't found the right moment, try for these romantic experiences:

https://www.walkaboutflorence.com/what-to-do/caffè-belvedere-bardini-garden

https://travelsacrossitaly.com/2012/12/06/marcos-florence-gregorian-chant-at-san-miniato-al-monte/

Keep getting feedback as you adjust your itineray. We want it to be perfect! :)

I like this new angle and do think the forum would rally to help you plan a perfect trip if you are willing to listen and make some tweaks.

I didn't even realize you are landing in Milan at first ; I see no point in going at all to Genoa then ; and a stop in easier to reach Lake Como in one of the pretty towns further up the lake for your 1st 2 nights right after the airport to me will be far more romantic than your idea of Genoa/Portofino.
It will also be more laid back and be a good first stop to get adjusted to the jetlag/time change.

From there train to Florence. Stay there, skip Genoa/Portofino/Pisa.
Your anniversary or maybe honeymoon trip can be to the coast, Portofino, Cinque Terre, etc... and Pisa is easy to include then as would Genoa if you want to.

Rent your car when leaving Florence, drive through Tuscany stop off at a few towns stay a night or two in the countryside before making it to Rome where you should/must drop off the car and then stay in Rome and train to Venice. Lastly taking a train from Venice to Milan as you depart.