I have a Probotix Nebula and notice the gantry has relatively low torsional rigidity and can cause the spindle to vibrate like you mentioned. By applying light torque loads to the spindle by hand I can see quite significant twist in the gantry and deviation of the cutter tip..similarly when operating, I can dampen the chatter during a cut by applying very slight hand pressure grabbing around the spindle housing.
The machine performs great overall but cut feeds and DOC I find must be significantly reduced, reducing productivity. I'm using new Amana carbide cutting bits and still see the problem. Not a very rigid design.
I'd be very interested to hear if you applied any structural work-arounds to increase the resistance to twist in the gantry frame. Apart from a complete gantry and hardware replacement with 8020 beam of larger sectional modulus, I was looking at what might be done on the existing 60mm x 30mm frame, maybe some type of structural tube/shape down the core of the section that locked into place from within.
Also, have you ever removed the gantry from the two uprights? I wonder about the two machine screws securing each end - perhaps these are a weak point in the twist as well since the torque loads applied at cutter tip would be transferred to these 4 mounting screws via shear.