You've only shifted through more than two gears once or twice? And, you did this while racing? WTF? So, you're telling me that you rev-match and slam it into third, fourth, and fifth with the clutch engaged? Likely story.

Did you try shifting into gear at the transaxle; that is, popping the hood and moving the two levers through 1st-Reverse? I probably won't work, but I figured I'd give you something to do while you determine how, where, and when you're going to get the tranny repaired.