Brass plug is what I've always had ... except when I fitted the Chinese Carb (for a few days) which has a plastic/nylon plug. So either one was "no change"
Compression test yes, many times ... But I can't see how a leak down issue would help with a starting problem? ... That's really an optimal performance thing.
Getting the valve timing just right does allow the engine to turnover without stopping on compression strokes. So that's important too.
Also I know it's a carburettor issue. Because I have another V-Twin motor (in another mower) and I swapped the twin barrel carb for the other mowers single barrel carb and the engine started easily.... I was tempted to convert the engine over to a single barrel carb ... but that would have been admitting defeat lol! ... Besides I learn a lot when things go wrong and I wouldn't trade that for the world!