The problem might be in the cable, that would be easy too.
But In order to properly assess the throttle you're gonna have to remove the throttle cap on the carb. You're gonna want to ensure that the throttle valve moves freely in the carb, and check the condition of the spring, position/condition of the jet needle, etc. Once you're this far, it's just another 2 phillips head clamps and a fuel line, and the thing is in your hand. You might need to loosen the subframe to loosen up the airbox, but thats easy with 2 seat bolts, and 3 subframe bolts if necessary.
Once the carb is in your hand you might as well clean it and replace worn parts. Especially if the bike sat for any length of time.
Just call up RMATV, tell them what you got and BLAMMO! 3 days later you get a shiny new toy/part in the mail for your kids dirtbike.
Install new carb parts into shiny clean carb and add new gas = bike runs like a raped ape = kid smiles = good dad
.
Easy peasy.
You'll probably get lucky and that idle screw will come out with the screwdriver like you mentioned, but if not I would be very careful with a drill. If you mess up the threads in the carb itself you wont be happy with the outcome.
I would try and unspin in it from inside the carb first, if I was able.
Also - it looks like you have a diaphragm thingy on the side of your carb. If the rubber in those gets old and gummy it will affect performance. They're easy to replace if you need to though, but they are pricey.