Distributor keeps adding advanced without stop?

Indeed, I have seen this before. It may sound okay and you may run with no audible pinging, BUT you will overheat the piston and if you run it long enough you will begin to deposit piston material on your spark plugs. (Ask me how I know!)
Yes. Too much advance under loaded conditions will have detonation that burns spark plug electrodes and piston crowns. Its always good to check the spark plug porcelain for tiny shiny specs of aluminum.
This will not show as more heat into the cooling system. Late timing will put more heat into the cylinder walls (piston is further down the hole during combustion) and into the coolant.
I too prefer timing tape or positively marking the balancer as posted elsewhere on here with a static timing light. Dial back timing lights are okay if you can afford a high end one, but I am weary of how delicate some of the electronics appear in a lot of the newer ones.
Part of the problem is the slew rate.

Maybe not.

I used a later model points (reman) distributor with FlameThower III and initially got numbers approaching 60. It must have been a lean burn dizzy originally. Regardless the 383 was not happy, welded up the diagonal slots just using a simple printed from the internet paper 360 degree template with a hole cut in the center for reference on the total mechanical advance. The particular motor setup as configured does not like part throttle with the vacuum advance so I blocked it with a BB/ball bearing. Total is now 35/36 with one light spring with 18 initial and the 292/509 motor loves it. Full advance by 2000. Controlled my temps at cruise and the motor has great response across the board.

Make sure the dizzy you have is compatible with the FBO plate before buying one!
Part throttle pinging is a common problem with vac advance when shortening the outside of the slots.
When using vac advance, shorten the inside and use the heavy secondary spring.