it sounds like things are going pretty well otherwise, and it's simply a question of everybody adjusting to the new situation.
Yet, it sounds straining as it is.
Can I ask if there are any complicating factors? For example, why is it that M feels like she has nothing to do when A spends time with you? Do they have a small apartment, like a studio (or living space arrangement where they can only spend time in the same room)? Only one computer/internet and nothing else for entertainment? What I'm getting at is if the problem for M is that A is not spending time with them
or if they are simply bored, and if the boredom is due to some aspect of organising their everyday life or due to M not taking enough responsibility to entertain themself.
If it is something concrete, start there. I'm in an LDR (similar time differences and all!) with one of my partners, and I really can't imagine having to skype with either of our other partners being in the same room. Privacy is essential for me, and I have arranged the furniture/living space in a way that allows that as well as possible.
Maybe it would be good to find out what it is that all of you want
the most, and brainstorm for a solution which would make everybody satisfied, trying to be as flexible about other things as possible; e.g. how much time you feel you "should" spend together for things to be equal - I don't know if that is something you tend to think, but I sure am familiar with that, and I think it can work better to focus on what people want and what works in the changed circumstances.
If I understand correctly, you identify that you would like for the time spent with A to interfere less with you spending time with your friends. And you aren't satisfied with the intimacy/connection you and A can establish in the current arrangement. M doesn't seem to be happy with the time they are getting with A (some of which may be legitimate and some not - I think it would be helpful if A would make decisions more on the basis what they want to do
and less on the basis of what their partners want. For example, in the schedule of 3-3-1, there doesn't sound to be any time for A to take to themself/their friends.) It does sound like you need to break the current scheduling in some way.
Just one suggestion: if, instead of 3 days with A you'd have 2, but focus to make those into really good quality time. The most important aspects of that quality time would be that it actually happens, only includes you and A, and will not be interrupted by M (whether they are home or not). That would, on one hand, free up some more time for you (and A) to spend doing your own stuff and, on the other, M might be more satisfied with that as well, and would be more inclined to give you privacy (although I do think that is something A should insist on, unless there are some space issues that make it really unreasonable).
Hopefully any of that is useful.
Let me know how it goes.