Flying into Rome but trip ends in Venice

Not that I am aware of. Can you not add an extra day?

Take the train directly to Venice when you land at FCO- much easier than flying and puts you right on Grand Canal, eliminating transit from VCE and worries about luggage and missing flight
Return to Rome at end, putting all your Rome nights at end
Eliminates split stay

You really don’t want to be flying from VCE to FCO on your departure day. Be in Rome night before.

No, you will have to do all the work so if you must keep the trip this way (rome at start Vs end), you’d need to fly back day before or very early day of flight home. We’ve done fly in day before, spend night near airport, then fly on home. It works well

Have these prices been consistent? I'd suggest setting up Google Flight alerts to track price fluctuations, and perhaps one day they will show up in your favor.
Safe travels.

Have you looked at the prices for flying into Milan (for us, always cheaper) and then immediate fast train to Venice, then end vacation in Rome and depart from Rome?

We have never found open jaw/multi city tickets to be more expensive other than a hundred or so and many times cheaper. So I am guessing that your are not looking at this correctly. But to prove me wrong I need to your departure city and dates of travel. And I would not do what you are asking -- too much risk.

Is this a scheduled tour? Or an independent Itinerary? Makes a difference to your actions.

If a scheduled tour, you may need to add a night for your return, an extra night in Rome doesn't suck, it's about 4 hours train time, lots of trains, so you could get to Rome on your last tour day, flying out the next day.

Independent Itinerary, then adjust, either save Rome to the end, or split your time in Rome to the first and last days, I like to spend the first night where, or near where I land, so I would opt to split, unless the next spot on my list was someplace like Orvieto, only a short train ride.

An edit: It is possible to link itineraries, depending on airlines and partnerships. For example, if you are Flying Delta round-trip to Rome, ITA (the Alitalia replacement) has joined the Skyteam Alliance, so you may be able to link itineraries with an ITA flight from Venice to Rome...but not Ryanair, for example. I think I would call before booking, and while they may link the itinerary and allow luggage to go through, they may not guarantee accommodating you if you should miss your connection in Rome (I seriously do not know, that is something to ask about)

Unfortunately the trip must start in Rome on a particular day (wedding) and end in Venice. It sounds like I will have to add an extra day to the trip, fly into Rome the night before. Will give me an extra half day in Venice at least!

Please, if you want help on flight schedules -- departure and dates -- critical. I did a quick search from Chicago, mid-summer, mid week, two weeks apart. RT Rome was in the $600 and $700 depending on schedule. Into Rome and home from Venice was in the $700 to $800 range -- About what I would expect. So your $1500 is off.

The fast train from Venice to Rome takes just 4 hours
Much simpler than getting to VCE for a short flight to Rome
You eliminate that transfer time/cost security/check, Etc
And you leave FROM city center and arrive IN city center
Stay IN Rome night before departure flight as long as flight is not at crack of dawn