Itinerary Assistance Appreciated!

this looks pretty organized.

Tips: get tickets in advance, whatever you can. IMHO, the fees of advance booking are more than worth the time saved in line.
Our favorite restaurants were Tapas 24 (http://www.foodbarcelona.com/tapas-24/) and 9Renas (an Argentine steakhouse) both near Gracias.
We did a great VIATOR for the Dali Museum. That is a drive from the city.

Eating early is hard in Spain. That was one hard thing to get used to, especially since while traveling you do not have time for a big lunch and you cannot eat too late since you're getting up early. But many places do not open for dinner before 8:30, unless they cater to the tourists. Adapt as much as you can.

Before our more vociferous Catalans criticise me, I should say that I greatly like Barcelona and think it is one of the best cities in Spain and a "must see" in Europe.

But
- La Rambla is one of it's worst sights. Terribly touristy and quite sordid at the sea end. If your hotel is near there then perhaps walk it on your arrival day, but otherwise just see it as a street to cross between quarters.
- Barcelona's cathedral is nothing special. If you've been elsewhere in Europe, you will have seen better. It is not an equivalent of York Minster or Milan duomo. For avoidance of doubt, I mean the Cathedral, not SF which is beautiful and definitely worth your visit.

So, put that time into what Barcelona does better. Definitely go inside some of the Modernisme buildings. The outsides are interesting but the interiors more so. You might also add Hospital de Sant Pau and the Catalan music palace. I would also consider the civil war museum in a former air raid shelter. That gives you a different view of Barcelona's history - arguably Cartagena faired worse, but it wasn't a good time up there either (or after).

And allow time for wandering the Montjuic and also along the seaside.

I disagree that eating "early" in Spain is difficult. And certainly not in Barcelona which is tourist central and has plenty of restaurants open whenever you wish to eat.

Saint Pau is a very easy walk from Sagrada Familia and well worth your time. You'll be seeing a lot of Gaudi's work and I bet you'd appreciate Montaner as well.

https://www.barcelonaturisme.com/wv3/en/page/1193/sant-pau-recinte-modernista.html

@Nick as a Catalan I am outraged! :)
Anyway... I agree with Nick on his points.

I also agree that to complement your Sagrada Familia visit you could also visit the Hospital Sant Pau, which is just a short walk away. Hospital Sant Pau is a Gaudi-esque modernisme complex built in the early 20th century. It has been named a UNESCO World Heritage Site and has significantly less tourists than the Sagrada Familia. My mom actually used to work there, before they closed down.

Also one nice place that (surprisingly) has very few tourists is Parc del Laberint d'Horta I personally like it better than Park Güell. The park is one of the oldest in Barcelona and comprises a fantastic 18th-century neoclassical garden with the centerpiece of a labyrinth made up of trimmed cypress trees. I used to go there a lot when I was younger.

A few nitpicky comments, which may or may not be useful:

• The way you've listed your plans makes it appear that you are going to teleport yourself from place to place. In some cases you will spend a good bit of time getting from one sight to the next, and I think your time allowances will sometimes be inadequate.

• Are the "select Gaudi houses" Casa Batllo and Casa Mila/La Pedrera? I'd allow a minimum of 90 minutes at each one, and they are not on the same block. Furthermore, even with tickets purchased in advance, you may stand in line for awhile. These are very crowded sites, and they appear to let people in only as others leave. I think planning just three hours for the two of them is very dicey. Those are expensive tickets, and I assume you'll want to get your money's worth.

• I think 90 minutes is about right for La Sagrada Familia only if you do not want to ascend one of the towers. I hope the Gaudi Exteriors tour ends at LSF. (You've done a great job laying out a geographically coherent sightseeing plan.)

• The Picasso Museum is the most crowded museum I've ever seen (haven't been to the Vatican Museums lately). I'd skip it if you're not a big fan. It's like those movie scenes of cocktail parties held in tiny Manhattan apartments--people standing elbow-to-elbow. You have to fight your way through the scrum to be able to read the labels posted beside each painting.

• I heartily agree with the other recommendations for Sant Pau and the Palau de la Musica Catalana. The latter requires a tour, offered frequently in English. So far no one has reported long ticket lines at Sant Pau, and it's great to have a sight in Barcelona to which you can simply walk up and buy a ticket. However, they're advertising more, and the situation could change.

• For me, Barceloneta is not special. I'd rather walk around the Eixample area, looking for modernista buildings, or go to the MNAC (Museu National d'Art de Catalunya). It has some lovely frescoes rescued from churches in the Pyrenees and an interesting modernism collection (furniture and decorative arts). Plus paintings and sculpture, of course. And the nearby Miro Museum is much more pleasant to visit than the Picasso. Those two are both on Montjuic.

All right, lets get this party started the right way.
DO NOT START WITH AN EARLY DINNER!
Reset your USA tummy clock and commence experiencing local culture by eating with the natives. Truly, grab some tapas, do take the long stroll, grab a cold shower, eat late and experience the local culture.
I will leave the daily recommendations to others.

Thanks everyone for your input. It is much appreciated!