1983 Datsun MAXIMA slow to shift into high gears. Works best with full tank

My car is in great condition. 70,000 miles and I am the second owner. Every time I take it to a mechanic they can’t believe how good the engine looks. But there is a mystery problem. I have been dealing with what seems to be an air leak or pressure issues. After driving for a while the car has a lazy start after a stop. The first few gears seem to not catch. If fells like there is a block in a line and it’s trying to push through air or fuel to get to the 3rd gear. I have noticed on colder days the timing belt screeches a bit. When in high altitudes this problem is worse! After my last oil change they noticed a leak. Also the dipstick for my transmission fluid is broken. Although I check it regularly and that seems to be just fine.
Any insights on this would be much appreciated!! I want to get to the bottom of this!

thanks!

KR

Let’s get to the easy stuff first. Timing belts don’t slip. What you hear is a drive belt slipping. These are the belts that drive accessories such as the alternator, power steering pump, AC compressor etc. Not sure if you have a serpentine belt on a 30 year old car. They could be loose or worn.
You say the transmission dipstick is broken but that you are checking it regularly. How are you checking it?
The first part of your post has me really confused. When you say it has a lazy start do you mean it feels like the engine has no power (doesn’t rev up) or that it revs up but doesn’t want to get the car moving (slipping transmission)? If it’s the second one and you say the transmission is leaking and it’s dipstick is broken you may be low on fluid. Are you checking the fluid properly? It’s not as simple as checking the engine oil. There’s a procedure in your owners manual.

Has the tranny fluid and filter been changed. As stated, a little confused on description.