If I wanted to take my 305 out and replace it with a 350 from the 60s or 70s, would the transmission still shift the same? Is there anything else I would need to know that I'll have to change for this swap? The car is a 84 Z28 LG4

The transmission shifts are decided by how your TV cable is adjusted. If you re-use your intake and carb, the way it is set now shouldn't change.

If you are running a different setup then you will need to re-adjust your TV cable to make it shift properly. Your repair manual will tell you how to adjust the cable.

If you run the LG4 ignition/induction system (only sane approach for a street driven car, IMO), then all you have to do is properly adjust the TV cable when you reinstall. Adjusting the shift point/behavior with TV cable adjustments is an absolute no-no.

If you don't use the LG4 carb, then you have to make absolutely sure the cable, bracket, and lever geometry exactly matches the q-jet configuration, or you'll be buying transmission after transmission.