We often do US and WDW in the same trip.
I'm a little unclear though, what are you doing before 1pm on transition day? Why 1pm?
Usually when we transfer between US/WDW or WDW/US, we try to do it early in the morning to take full advantage of our tickets and FP/Express Pass.
This is especially true in summer, so we beat the afternoon heat and pop up storms.
Universal is pretty laid back. I personally don't even see a reason to limit yourself to just one park if you have hoppers. If anything, the Hogwart's Express is the probably the most mellow ride on all of Universal property, and the ride is different in each direction. It is a very easy and mellow way to transfer between the parks, if you wish. Universal is more compact than WDW, so walking back to RP from either park is pretty easy.
You'll likely want to start at IoA if you walk over, because it is slightly closer to RP, but all of Universal is very walkable. Shuttle boats are also frequent. If you take the shuttle boat, you might want to start at US, because that's slightly closer to the boat dock. If you do that, then you can take a picture in front of the iconic US globe!
When we transfer between hotels, we try to mostly pack up the night before. At both WDW and US, you can check-in before 1pm, just don't expect your room to be ready until the afternoon. (though it might be ready when you arrive.) Either way, you can leave your bags with bell services.
Of course, RP is also a very nice place to spend an afternoon! If you decide you'd rather do that...maybe swim, explore the other resorts and/or Citywalk.