Apparently that's what is already in the box and he did try a number of oils in the time he had the car..
3-2 is not a difficult shift either at this stage - it's an impossible change without rev matching
I've actually created this problem myself once years ago in a supercharged V8 with a brand new 600ft-lb gearbox after trying to shift hard at high RPM with a badly adjusted ceramic clutch
and I had to replace the gear, collar and synchro. The teeth were flattened just enough from the grind that there wasn't enough of a point in them to index the ring.
There's a good video on youtube where this guy explains a blockout condition and causes. Granted the teeth might be ok and it could be also be the keyway. But at this stage either way there's disassembly required, unfortunately!
https://youtu.be/MXsRfbOiBhE?t=228