The fact the carbs have been rebuilt and assuming the bike run fine before whatever made you rebuild them? I would suggest you start there first, air leaks, check the choke lever and the plungers on the carb bodies are fully returning it will only take one to give you the symptoms you've stated. It could also be incorrectly set/fitted needles, diaphragms, jets and pilot screws and balance. Failing that check the air filter intake and the filter it's self, if it's still there it could be a series of other issues, but the fact it's starting and running albeit not as it should rule out a lot of what you think it might be.
The race can will have no effect, Fazer are rich as standard and fitting one cleans up the low/mid range fuelling.