It runs just fine at 165 hz for me. Given that xrandr and CRTs have been around for a while, and both have supported high refresh rates for a long while, something seems fishy here. Something is probably at fault, but it's not X11.
(Hint: It’s not possible to solve correctly.)
Couldn't you stop tearing with a couple lines of code? Don't swap out buffers mid-frame, very simple.
The simple solution doesn't make 144+60 look super smooth, but 120+60 should be almost perfect.