Firstly, the '55 transmission is totally different from the '56 and later designs (thank your lucky stars).

Changing the fluid is a good idea. it tends to get gummy with that much standing around.

My hunch here is that the control valve body in the driver's side of the transmission is all gummed up.  Since this is one of the late Hydra-Matics that's rotated, there will be some different way of removing the side cover of the transmission, from the pre-'54.

The control valve body is held on by cap screws, and is easily removed, once you've opened up the cover.  You will find several little spool valve plugs in it, which cause the transmission functions, such as shifting.  I believe that you'll find them sticking in their bores, from gummed up oil.  Get the bores and the valve plugs clean, so that each plug will fall through its bore by gravity.  Replace the valve body, button up the transmission, and it should shift like new.  I'm assuming that the neoprene seals for the clutches haven't hardened and cracked, so shifts should be smooth, and sharp.

This applies to all Hydra-Matics, before 1956.  Sticky governor plugs cause a rough 2-3 upshift. You'll never find a valve body, where the plug valves move freely!

THE (APPARENT) SOLUTION -  DRIVING THE CAR FOR 5 MILES, WITH A CAN OF Sea Foam Trans Tune IN THE TRANNY.