In this transmission, the 2-3 shift is very tricky, and as Otto has already said, it (could be) harsh. It really should not be.
Since the car is a low mileage one, my advice is to take off the side cover pan, and remove the control valve body. Best to have a shop do it, as it's messy, especially since this transmission is rotated a few degrees. You will almost surely find that the little valve plugs in the valve body are hanging up on a varnish that has formed in their bores, over the years. They should slide along their bores totally by gravity, and not hang up anywhere.
In those transmissions, the 2-3 upshift involves whatever clutches are off, to engage, and whatever bands were applied, release, etc. In other words, EVERYTHING in the transmission changes in one instant. That was one of the trickiest parts of the transmission's design, but they perfected it.