Another angle: let’s consider the transition between Scene 1 & Scene 2.
“Copy~Paste” the elements~animations at the end of Scene 1 into Scene 2’s start; or duplicate Scene 1 and eliminate all the Scene 1 elements in this duplicated Scene (which will now become Scene 2) except those elements that will appear at the very end of Scene 1.
So at this point we have Scene 1 with all of its elements & animations; and Scene 2 that features all the elements at the end point of Scene 1 located at the beginning of Scene 2 - just where the “transition” would be starting.
Set the transition from Scene 1 to Scene 2 to be “instant”. The net effect for the viewer is no recognizable difference between the end of Scene 1 & the beginning of Scene 2.
Now create your crossfade transition in Scene 2 using the elements of Scene 1 which can be animated as they fade out and the (new) elements for Scene 2 that You can animate as they fade in - because the “transition” is actually occurring in just one scene (Scene 2).
This way You do not need to put everything in one Scene and can work with Hype as usual. Of course, You will also need to use some design sense. The best~easiest place to make the Scene jump should be a place of relatively static behavior of your stage elements - so design your Scene transitions accordingly.