I think I've, like, said everything in this post before but I had nothing better to do so I typed it up.
I heard RI warping was hard. What you should do is just try doing it for practice. Try and get a feel for the timing as you run up to the blue warp. Probably try BA to learn the timing for actually warping (it's a lot harder for adult dungeons, but iirc somewhere near the end of the fade-out is multi-frame window). If you can get it sometimes, try just casting FW somewhere in your runs (possibly the dungeon entrance since you wouldn't have to RI, but maybe somewhere closer to where you'd want to go next) and just make an attempt at it?
For Fire you're going to need a cutscene to warp into, but I can't think of anything worth warping into. My best guess is that you should warp into the door of time opening cutscene. Since the door is already open, it should be super short, and it's possible that LACS will play instead, if you do Fire last. If you can't find a good entrance to use to warp to ToT without entering the ToT, you'd use Outside ToT->ToT (unless LACS->ToT doesn't crash). Looking at the WW table, the best I can really see is Desert Colossus->Fairy Fountain, so IDK if that's faster than just doing the extra savewarp and then watching the shorter DoT opening CS later (this is assuming LACS really does play instead). Fire Medallion CS isn't really that long, though.