Welcome from me as well.
There will be ample reading on morning sickness. Just use #xj in the search function, and include the BW66 in your reading as these boxes are very similar. Frank is a great help as well.
The transmission is determining shift point and quality via the throttle position. the further the cable is pulled out, the higher the rpm and the harder the shift process itself. It is important to get the pressure right, otherwise the transmission won’t last long. I wouldn’t mess with the cable by trial and error, but it can be done theoretically. I did it with a long hose and a pressure gauge, not as hard as I thought. That for now.
If you did check with the engine running, in park, after going through all positions, the fluid should be okay (Type F is recommended and Dexron III gives softer shifts at the cost of shortening the life of the friction elements, so it is okay, just not the best choice) you shouldn’t worry about fluid levels and look for what happens when the seals go bad or the pump pressure / governor pressure drops off for any reason. You implied that it gets better when it warms up, so it must be more of a temperature thing than adjustment related.
I don’t recommend that you do this but if you removed the throttle cable (don’t push it in, lest if slips off inside the transmission, tie it up somewhere in a just slack position), it should shift very early and very soft. Not good for the transmission, but as a test. This would indicate that the system operates well and the cable is maladjusted. Better if you read up first and find better reasons for your behaviour.
One thing, what did the old fluid look like?