When a bunch of these were getting installed back in 07-09, I could swear I remember people having to rock the car, in-gear, engine off, until it came unstuck. Issue happens during shipping. Would try that before you cut anything.
I don't mind my TKO shifting, but it's no T56 and it's better than the M21 4-speed I had before. I bought it for the overdrive, and that's the benefit I got from it.
You should be able to shift it sitting there. Especially with the clutch pedal pushed in. You can have someone depress the pedal and check for air gap on the clutch. Take a .020 feeler gauge and see if it will fit. I don't recall, but I think the TKO 600 likes .060 of air gap for best shifting. Bottom line, with an air gap, the trans should shift. I do recall one other person having a two 600 get stuck in gear. Maybe it's related.
I put carbon fiber synchros, shifter, and adjusted the air gap, I still wasn't happy with mine. They are strong and it may suit you fine. They just don't shift quickly and at high rpm well.
Have someone press the clutch pedal, then climb under the car and see if the .020 feeler gauge will slide between the clutch and pressure plate or flywheel. If it does, you know your clutch is being disengaged. That leaves it to internal transmission issues.