I usually find that LME is so taxing, an effective max strength workout isn’t possible.

So I do what you described: Develop max strength before ME, and then maintain it during.

In particular, two sessions of each would be a huge load. I suspect the quality of one or both would suffer, especially because a key part of ME training is maintaining your aerobic capacity training. If general endurance training starts to decline in volume, then the ME load is too much.