Hi, Robert
First off I want to be clear that I am not a fan of the Balcar mount either. It's definitely not my favorite among the several mounts I have used over the years.
That said, I switched from Bowens monolights to e640's back in 2012, and with the three Einsteins I now own I have never experienced one drop. Since you mention that your drops tend to happen after the modeling lights have been on for a while, could you possibly share what adapter rings you use? I am wondering if the rings are softening as they heat up, allowing them to go "out of round" and playing right into the weak-suit of the Balcar mount.
When I switched to Einsteins in 2012, I chose this adapter ring to fit into the Bowens Quickrings in which I was already invested and liked very, very much:
http://www.bhphotovideo.com/c/product/185322-REG/SP_Studio_Systems_SPARBW1_Speed_Ring_for_Balcar.htmlI regularly boom my Einsteins as seen below, and this is a fairly heavy rig: a heavy-duty, 60" eight-rod Visico Octa with an inner diffuser, outer diffuser, Bowens Quickring, and the SP adapter linked above. I've never weighed it, but it's a load to be sure; it requires a steel stand and boom, and 15-20 pounds of counter-weight. I've also used the same setup in studio with a grid (adding even more weight) and with the modeling light on, and have not had a drop in that scenario either.