Really weird ignition issue...

It doesn’t explain why the car runs terribly with the vacuum can connected.
I think it does explain it! You’ve diagnosed a vacuum leak on the vac canisters.

Where the arm comes out the back of the vac canister, there’s a hole. With the engine running, spray some brake, carb cleaner, starter fluid whatever in the hole. Put the nozzle right in the hole. Any change in idle indicates a leak.