I agree that it's not fair that you have to have National 5 Maths in order to get into a lot of uni courses, but it will honestly be worthwhile just in case to take maths. I think taking both Modern Studies and politics would as stated before, be like taking Biology and Human Biology, so i would choose Modern Studies. This, I see however will make you unable to take Drama if you want the MS and History combination along with it.
This happened to me in school also, however my subjects were vastly different from yours - I took Maths, Physics, Graphic Communication and Computing Science. I ended up having to drop Art in order to take computing science, as they were in the same column and i wanted to be an engineer or something haha currently doing my degree in Engineering. The point is, do what you want to do as long as its beneficial - if that makes sense. It would be fine for you to take drama, provided you definitely take history, as it is very important to all of your degree aspirations, obviously history. French does look very impressive on your CV and it will open doors for you. English is essential for all of your degree choices, it is a must have, although English is in all of your cominations so that is fine. I assume you are a very Arts based person, which works to your advantage, as i see you are dropping Biology. I would suggest that you take -
Higher French
Nat 5 Maths
Higher Modern Studies
Higher English
Higher History
Edinburgh generally only requires 4 highers anyway, with the exception of Medicine and such, so give yourself a break. Do 4 highers instead, 5 is a lot to handle, especially the subjects that you have chosen, which are primarily essay based. If you only need 4, do 4. It will help you to focus better. Keep English and History definitely though, you will need these two for the things that you want to do. Long reply, i'm rambling. Good luck and try not to get too stressed out, you have next year for all of that hand cramp. Good luck with your exams x