Both the nylon speedo gear and the worm drive gear are different between GT Apex and other models, which is, unfortunately a pain in the butt.
I'd make sure of a few simple things first, like that your speedo drive still has the clip in place that holds the gear and shaft in the speedo drive housing so that it's not launching itself into the gearbox for fun. I've seen it a few times before.
If you really want to spend alot of money, get the box pulled apart, inspected, a new worm drive gear put on and a new speedo nylon gear.
Most sane people wouldn't do that as a diagnosis step though