Linear encoders won't help with the sudden droop. I have the same problem with Z gouging. Its the Z slide slipping / sticking coupled with (in my case) a single ballnut on the z( few thou backlash) and the top angular contact bearing block / bearings being crap (from Chai) having slop as well.
I haven't come up with a good solution so far, for small light duty stuff (1/4" endmill or less) I set the gibbs looser so the head doesn't pull down as soon as you start cutting.
For heavy cuts I whack the head down before it engages the part - neither is good for an automated cut or in a pocket.
Not sure if a counterbalance setup would help with the stick - slip if it was positioned so that the head was properly balanced and not cantilevered off the column? Looking forward to see if you have a solution that works (and is cheap)
Mike