I don't have any problem shooting several different recurves from 50#-55#.  I shoot them all with a T-300 rest set the same distance off the shelf on the sight window, using the same arrows. The elevated rest is very forgiving and as it's the same height off my hand on all there is little difference in POA/POI...

I shoot my hunting bow daily. My other ten bows for the most part, get shot less than once every two months. (just for fun) . My goal is to take game with my bow. Alot can happen in a hunting situation and I want to be confident with my equipment.

Been thru alot of bows and by your discription of the bows you shoot,I feel a couple reason could be the reason for the difference in impact.
(1) your LX longbow is some what heavier draw weight
(2) different grip style from your other bows.

I've recently went thru the same and when I got comfortable w/ the heavier bow they all came together w/ point of impact.

Whats kinda funny is the LX at 66lbs is a tad slower with the same 600gr arrow as my zipper 60lbs.    I thought it was faster, but I shot em thru the chrono today.  I got 185fps with 600gr arrow, and 164fps with 700gr arrow.

I have 3 bows that are all within 2 lbs draw weight of each other. I can shoot the same arrows through all of them. I really don't have to worry how I have to adjust my shooting when going from one to the next. This is all after have limbs that were from 45# to 60#.  This works for me now.