I think this could actually work very well, so long as you are aware of the specific difficulties and solve them:
- The events in the various universes will have to be independent from each other. That's no problem so long as you are aware of it and don't try to fight against it. Just make it a series of essentially independent episodes. In the same way that Star Trek - The Original Series had stand-alone episodes, each dealing with a monster of the week, you will need to create one stand-alone "love interest of the week" story per universe/franchise. I would start with some of these, and try to make each of them recognizably in the style of the respective franchise.
- Once you have a few episodes, you can think of the details of the framework story connecting them. You will then know what you are working with, and you will have some useful experience before you start on the framework universe that people will see at the beginning and end of every episode. Sure, there should probably be some cases in which the framework story and the episode are connecting in non-trivial ways. But it's probably best if that's not always the case, and if you start with the regular cases. (In terms of creation order. Even if you first release a series of disconnected episodes, you can later reorder them as you develop the framework story and embed them into it.)
- Regarding the problem with the models: I would solve this by using the same 'cast' of models (like actors/actresses) for all episodes, just varying the costumes. If you know the European Disney comics, you may already be familiar with the concept. There is a large number of comic strips that are parodies of classical novels with Donald Duck and his nephews, Uncle Scrooge, Daisy, Mickey Mouse, Goofy, etc. all playing the roles of the original protagonists. The tension between the 'natural' behaviors of the 'actors' and those of the roles they are playing are a good driving force for making the parodies distinct from the originals. But even if you don't make much use of this, you can at least reuse the models. Don't bother creating an in-universe explanation why people in different universes look eerily similar. I can't remember what it's called, but I am sure there is an article on tvtropes.org that explains how to deal with such plotholes through the simple expedient of making a character comment on how strange it is. That turns it into a mystery in-universe, and there is no need to save this mystery.