Welcome to our forum.
From what I can read and perceive from my point of view, there has been some gaps in communication, and L's long stretches away from home are a big problem in the first place, even if the "M situation" wasn't piled on top of it.
It is a concern that M has (seemingly) resisted your efforts to meet with her. I don't know whether she can be trusted. It's possible she's a psychological mess, an extension of her obviously messed-up marriage.
It's not fair for you to be put in this situation, but make sure L understands exactly what your needs are here. I would start by telling him that his job is a problem, because really I think it is (though not perhaps due to any fault of his own). One way or another, you need more time with him.
He is obviously caught up in NRE and to be fair, M probably is too (even if she is manipulating the situation). L and M both need to slow it down and work on their respective marriages. But it's hard to explain that to someone whose head is spinning with NRE.
I don't envy your situation, but I'd probably say the above are the main points that need attention for the time being. Certainly I think you're getting a crappy deal, and my heart does go out to you.
I see possible (probable) drama increasing in the future before it decreases. M's marriage may not survive this (and as you said, even you have questioned your marriage). I wish there was some way to warn L and M about the perils of NRE, but they seem determined to learn it the hard way.
Talk to L, tell him you need him to slow it down with M, and that you need more of his time and attention. It's highly unfair of M to be ringing, texting, and emailing L on his rare days alone with you.
You'll have to try to close some of the communication gaps, because L isn't stepping up to the plate right now. Until he comes to his senses a little bit, it will probably be mainly you who is working to save your marriage.
So sorry this has all happened. I can only give you my perspective; I can't tell you what the right thing is for you. I'm sure you'll be doing considerably more thinking about it, regardless.
Love means never having to say, "Put down that meat cleaver!"