I think you have a couple different items in your questions. Sorry if you already knew this.... First, remember that
Genie+ and ILL$ are separate, so you do not need to purchase Genie+ to make an ILL$ for Remy at EP. Second, while Genie+ attractions are shown with 'next available' time slots, ILL$ has some flexibility in allowing you what time slot you'd like to buy it for (similar to the old FP+ system) - so you could potentially buy a Remy ILL$ for that evening. If it were us, and if I understand your situation correctly, I'd get a park reservation for EP (or evening another park and then hop to EP, if that's an option), buy an ILL$ for Remy for the evening, forget buying G+ that day, and enjoy many of the attractions later in the day and into the EMH. Of course, that's just one plan to choose from!!! I'm sure you'll get other good ideas, too. Enjoy your trip!