Engine dies when warm

I did not set the timing with a light because the tab on the timing cover has broken off. I found TDC and got it as close as I can. While the car is in park I can mess with the throttle and bring it up to any rpm without a problem. Wouldn’t incorrect timing cause it to die when I do this no matter what gear it’s in?
You are going to have to fix that.

Alternately you can accurately find TDC and make a new mark on the balancer or front cover.

As for not happening without a load.
If the timing is anywhere close it will run without a load but load up the engine and then the timing needs to be correct.

Have you checked to see if the vacuum advance is working? When you hooked it up to manifold vacuume the advance should have gone up and the rpm should have gone up significantly