And here are 2 more bits of information. Both the 350 and the 346XP use the same cylinder base gasket, #503894401. And I believe the same carb as well. So, I'm pretty sure that this will work. It would be a 346XP where the "XP" stood for "Xtra Plastic"!
And believe it or not, the price for a piston and cylinder for a 346XP is $38 LESS than one for a 350. ($170 vs $208 list)
There are an awful lot of dead 350's out there. Obviously, it sells in huge numbers, but also because a great many of them are bought by novices who are more prone accidents, straight gas, and such.