The ski doesnt die, it will act like it wants to get back on it, but then boggs down again. The carburetor was rebuilt, when you choke it, it dies, so I know its getting fuel to the carb.
The rectifer changes AC voltage to DC so the electronics can use it.. When the engine spins the magneto generates AC voltage just like a generator.. So if it's not working you will not get the needed voltage to charge the battery and run the ski..
is the battery going dead on you? the regulator rectifier is part of the charging system only and with a fully charged battery your ski will run fine till the battery gets low IF its the voltage regulator. if you arent having to keep charging the battery then its not the voltage regulator.