@Titan-682 okay well first think of other dimensions that is connected with the universe she is in.
And the focal point will be her earth but instead of other worlds being in different multiverse why not have it be in different dimension where some are connected with Earth.
Like think of the 9 realms from marvel mythos of thor or God of war 9 realms and how they are connected.
Find a way that it can be connected for at least some of the franchises you are adding.
Well let's start small first think of the first arc and then build up what you plan later on in the second and third.
I would say for earth think of a number of what earth for it and that can include the Godzilla stuff, marvel and marvel rivals, SCP mythos, AOT(here you could say the Greek gods made the titans as a form of punishment), Hachishaku.
This can be in the world however the other dimensions that is connected to earth like mudguard(it be a variant of earth God of war version and the nine realms and the marvel asguardians will exist however the god of war version will exist to just it exists in a dimension connected to earth).
Invincible will also exist in this world.
But the other stuff the problems you have I say instead of simply multiverse travel or getting stuck instead there be dimensions connected to earth and to their worlds as well and in a way it not in other multiverse.
And you could have it be connected with how monster verse have that energy to get to where skar king is and the other apes were.
Also again use franchises connected to earth right now and a bit later on Gojira or whoever will discover more of the energy and be able to go to the different dimension that is connected to earth.
That way you can also say why earth is so interested by multiple people and enemies cause it be a doorway to different dimensions.
Tell me you understand and I hope this help.