You've probably been there already . . . but what's the float level like?
With the replacement carb, could you be suffering from the old 'Does it or doesn't it need a washer between the banjo and the float chamber?'
A lot of us have earned that T shirt.
I don't think this is primarily a main jet thing, unless you are running at big throttle openings all the time. (I think Musky said that somewhere earlier in the thread too.)
Too big a pilot, wrong slide cutaway, plus position of needle groove and size of needle jet are more likely to be relevant I'd say, if the fuel level is good.
The bits you've got don't sound daft and certainly don't suggest you should need the chimney sweep to the extent your picture says he's needed!
Most boggish-standard 500 twins with a 376 Monobloc will run somewhere between 220 and 260 mains (no air filter), a .106 needle jet, and a 25 or maybe 30 pilot, with a 3, 3.5 or 4 (some marques) cutaway, and not be stupidly far off. As you go down towards 200 for the main you're entering Concentric territory, or even pre-Monobloc, where smaller is typical. Hence wondering about float level.
One other thought - is the needle stamped 'C'? There are shorter 'B' ones used on 375s and that would make a heck of a difference if it was wrong. Got that T shirt too.