
I get you. It's really tough to do anything while you're fasting, let alone study for something as mind draining as the MCAT.
I've been following this schedule that's worked out very well for me so far this Ramadan. I find it's often easier to just study during the night and push sleep off till the day. I don't know if you have that luxury (work, etc.) but that would be my recommendation. However for us Fajr is a lot later (almost 5am) so I can get almost 5 hours of studying after Taraweeh. I'm still doing content review and haven't moved on to FLs yet.
Another recommendation would be to study immediately after Suhoor, so around 3 ish for you. If you have a decent meal with good amount of Carbs ( I would recommend brown rice and fruits!) you should be able to study for a while before feeling the effects.
Hoped that helped. Best wishes!