I appreciate your willingness to offer advice but the tractor is not functioning as it should. Two mechanics, the service manager, the salesman and I all agree about that. They're asking a Deere area rep to get involved and we're all hoping to find a solution that makes it right. The issue is not that I'm operating the tractor incorrectly or asking it to do anything I wasn't told and we don't agree it should do.
As far as how I'm using the hand throttle and brake pedals, that's just what you do to steer a tractor when the front tires don't have traction enough to steer, both 4wd and 2wd tractors, the same as you would do to steer a backhoe under the same circumstances, if you're more familiar with that. It's very useful when doing loader work, especially grading, backsliding and plowing snow.
Again, if the transmission shifted smoothly and the brakes worked on first push, all would be good.
Incidentally, since the re-calibration shifting from reverse to forward is very smooth, as should be expected. The problem remaining is only with shifting from forward to reverse; at any speed including standing still at an idle, without using the clutch or changing gears or ranges.