BMR is awfully low. That's how many cals you would burn if you laid in bed all day and did nothing! You seem to have pretty intense workouts. Honestly I don't think you are going to gain much muscle on this plan.
I get what you saying about body recomposition, i.e., more calories on strength days and less on cardio days. But I would probably eat more than your BMR. I can't really tell you a specific number since I don't know you and how your body reacts, but you are probably right in saying that eating the equivalent of your BMR isn't realistic.
Yeah, I'm following my body's lead on this one and eating whenever it craves food. Yesterday I was planning on eating just my BMR but found that I would have gone incredibly hungry for half the day had I done so. I'm kind of taking it one day at a time for now and don't plan on doing anything too extreme. I think it's usually best to follow one's common sense, like the more one exercises or exerts oneself the more one needs to intake in order to recharge. Thanks for the confirmation on my decision, because it makes me even more sure I'm on the right track. <3