The B&S engines of that era had a quirk known as "easy spin starting" that was a sort of built in compression release that brought on problems with shutting down or failure to start when hot.
If you watch carefully, just as the piston comes up on compression stroke, the intake valve, just for an instant, raises just a tad and closes again, letting off a portion of the compression. One of the very best things a guy can do for those engines after they get some wear is to increase the valve clearance a bit....maybe an extra .010, although the amount is not critical.
The usual pattern causing problems is that the valve face wears against the seat, eliminating any clearance that exists, and as the valve heats up it's effective length also increases and that persnickety low clearance that allows the "easy spin starting" scheme to work is just too small when everything is hot and the valves never fully close at operating temperature.
Removing as little as .010 to .020 from both valves at the end that connects with the valve lifter will increase compression enough that you can actually FEEL the difference in resistance at the starter rope, AND in the fact that the dang thing keeps running when hot......Joe
@ol'joe - There's something I want to add. Yes grinding the valve stems will counteract that compression release, but also consider that it actually DECREASES valve lift, so there's really not much to be gained by that method. Also please note there's nothing to be gained by modifying the exhaust valve or lobe, it's only the intake valve that relieves compression.
However, I have taken a 3 HP Briggs flathead and hopped it up a bit for free. I encountered the compression release as well, and my solution was to actually take a file and grind off a bit of the LOBE of intake lobe of the cam. Not where it opens the valve, but the very slight bump that actuates the Easy-Spin. This method bumps up the compression and takes advantage of the whole compression stroke, plus keeps the same valve lift.
After doing that to the cam on my engine, plus some other mods, the l'il 3 horse is a THUMPER! It feels noticeably more powerful and runs strong. It's a little harder to pull over, but I like being able to feel the distinction between strokes anyway.
@aliusa - It may be a good idea to check your valve lash with a feeler guage, sometimes that can make an engine do what you're describing.
Also, black oil is not necessarily bad, it just shows that the oil is doing it's cleaning element. Now metal shavings in the oil, on the other hand(little sparklies), are VERY BAD.
We need to determine if you have ignition points or the modern Magnetron coil. Look at my 3rd picture, do you have a wire going behind your flywheel like my engine?