I'm no expert and haven't worked on a PowerGlide in decades so bear w/me.
Trace the vacuum line down to the tranny, it will lead you straight to the modulator valve.
Have you changed the tranny fluid recently or add any? Did the previous owner tell you what fluid was in it? i.e. Type F or Dexron, Dexron II etc.? Sometimes mixing fluids can cause problems.
Since you can manually shift to neutral and not stall the engine, the tranny "may" be all or part of the stalling issue.
On these older auto tranny's, the kickdown linkage is used to shift the tranny from high to low when you floor the throttle pedal giving you increased rpm and power. Again I'm no expert and it could be possible if not probable that the tranny works fine without it connected. I do know from past experiences that it needed to be properly adjusted for the tranny to shift properly in "stock OEM" applications.
The problem could still be engine related, the easy checks I recommended are just some troubleshooting tips to try and isolate the problem.
Good luck
Dave
