Here's another idea - your stock tach is probably way off. I've seen these tachs off by as much as 500 RPM at 6000 (my own '90 coupe is 500 too high at 6000). You might think you are shifting at 5500 and are actually shifting at 5000. It will help for you to use a good tach, even if it's just a temporary hookup, and find out what RPM you are really at when your tach says 5500 or 6000.
Secondly, the 1-2 shift should be at the red line, just before fuel cutoff. There is no place in second gear that is better than any place in 1st for acceleration. Your 2-3 shift should be lower, probably in the 5500 range. You should not allow the car to go into overdrive - run it out in D. There is nothing wrong with manually shifting the transmission either.
-Matthew