You have 2 problems which are not really connected.
Excessive blow back through the carb is causes by a bad valve or blocked exhaust
Inlet is not closing fully so the compressing charge is being blown back out the carb as the piston rises
Blocked exhaust / exhaust valve not opening the cylinder may fire but the exhaust can not get out so it stays in the cylinder till the inlet opens and then blows back out the carb
Bring a side valve it is a PIA to get to the valve chest & observe so probably easier to pull both heads & watch the valves moving.
When I suspect bad valve timing but can not be sure I move the magneto (s) back off the flywheel then put some masking tape around the flywheel.
Then I do 2 full revolutions of the crankcase marking when each valve starts to open, is open fully and closes plus the piston when it is at TDC & BDC
Then I carefully remove the tape . lay it on the edge of some graph paper and plot the valves as a bar graph then plot the piston as a zig-zag line over the top.
While B & S do not publish their valve timing ( where I can access them anyway ) you will easily see if the cam is mistimed, one valve is not moving as it should
If you have a cheap vernier gauge with a depth gauge function then use it to measure the maximum valve lift , they should all be the same, within the limits of valve lash which on your engine is +/- o.oo5"
second problem is that carb
It is flooding .
To say they are a bitch to work on is a massive understatement .
I could write 40 pages on how to work on them buy their are a lot of You-tube videos that can show you how it is done , but it ain't easy
