About cheating -- you know, there are folks (mostly weight-training types, I think) who deliberately load up on carbs once a week or so, just prior to an intense workout. (I guess it's a version of the old "carbo loading" that marathoners used to do.)
They seem to think that periodic carb loading, combined with intense exercise, both accelerates fat loss and helps build muscle.
I don't know much about it, apart from having surfed a few pages in this forum, but I think it's called "cyclic ketogenic diet" or something like that . . . .
Maybe I'm irresponsible in posting about something I know almost nothing about -- but go check it out. It's possible that that a "cheat" is not necessarily a "cheat" depending on your point of view. If you find yourself deviating from your LC plan for a day or so, you could always try doing what those folks do (I'm not sure on the details but I believe it involves intense exercise within a few hours) and you might even BENEFIT from your "cheat."
Sadly, the one time I cheated was at a weeding where I had a wee bit too much to drink and not only couldn't exercise that evening, but was sidelined by a hangover the next day as well, so I couldn't exercise so was prevented from doing the experiemnt, myself.