You may want to try a different shifter first but it sounds like the transmission is having issues too. GMM Ripshifter is the best according to the really knowledgeable people on this forum but it's the most expensive too at near $500 these days.
You may eventually have to take it to a transmission shop for overhaul. I had the same problems you're having and several of the synchros were worn out, especially reverse and it was hell to try to get it in there at times. 2nd gear was bad too; I experienced a crunching noise every time I tried to shift to 2nd under power. I got an upgrade to carbon and bronze parts to handle extra power but the standard overhaul should make a world of difference. It won't be cheap (of course), probably about $1500 but sounds like that's what you may need to do. Lots of owners never have issues as the T-56 is really a good, solid transmission but has a lousy stock shifter (in the gtos) that doesn't help and you never know how the previous owner(s) treated the car before you bought it.
1-7/8" ARH LTs, 3" Magnaflow exh.,Spec twin disc clutch, 402 stroker , Fast 102 w/Nick Williams TB, 1000 hp shaft & axles, cam, fuel & suspension upgrades. 500 rwhp, 484 rwtq