Denny,
As far as the vacuum advance goes, you have it a little wrong on the operation. The mechanical advance starts at a given rpm and quits at a given rpm with no input from the vacuum unit, Chevrolet set these points for optimal performance. The vacuum advance is pulled all the way on at idle and backs off as the vacuum drops. So with your timing set at say 10 degrees, the vacuum will pull it in to 20 degrees or how ever much it pulls. You could have as much as 35 or 40 degrees of timing going down the level road. All this is factory set for a reason.

You have stated, that one system takes over for the other at a given rpm, this is false, they both work together, all ways changing and adapting. You want the maximum timing the engine can handle for the best fuel milage and emissions. All new cars with computors run the timing right at the point of detenation, this is the optimum point for economy.
Under a load, the vacuum drops and the timing backs off, for maximum power even if the mechanical is all the way advanced.

Depending on the model, the vacuum might be hooked above the throttle shaft or below it. Below the shaft is full time vacuum, which helps the engine idle better with more timing. Above the throttle is ported vacuum, which pulls the advance in as your open the throttle. Either way both systems work together.

As far as your hesitation, a vacuum leak will cause a lean condition which will cause a hesitation. A really bad vacuum advance unit just might be enough of a leak if you are on the edge of running lean already. Check around the intake ports for a leak or the base gasket. Something is changing with heat. One of your backfires could have blown out a gasket that was good not long ago.

Joe