The carbs should be disassembled to clean, you just don't have to split the whole rack into individual carbs. It would be a good idea to get a rebuild kit for the carbs unless you know for sure this has been done recently. Something else to chew on... What did the plugs look like? As your engine warms to operating temps it requires a leaner fuel mixture than when cold. If your carbs are allowing too much fuel into the engine, it would run worse as it warmed up, it could be a jetting issue. If it was riding fine until now you may have a jet that has fallen out allowing too much fuel. Carbs that need cleaned from sittng around too long, usually, have a problem from the get go & run better (if at all) as the engine warms. Either way, sounds like the carbs need to come out. Again these are just bits of info for you to consider. There is much more to consider to give you a complete diag. Hope this helps!