20,000 miles is a little soon for a new injector to go bad. What comes to mind is the possibility the fuel filter is letting sediment by which ends up plugging the fuel injectors. If the engine is not running properly, it would be difficult to diagnose transmission problems. The 60,000-mile service probably includes replacing the timing belt. Sorry we wish we could help you more.
Special equipment is required for proper cleaning.
You might want to try a gasoline additive for cleaning fuel injectors. However, make sure it is compatible with the catalytic converter. I don't know much about cars, but from what I could tell I was not getting any fuel, because the car will start, for a few seconds when I pour gasoline, into what looks to me to be the carburetor. Anyway, I replaced the fuel pump, which definitely was faulty. I am now getting fuel almost up to what looks like a carburetor.