Spark plugs are wet, needle and seat are good, carbs are cleaned. What next???
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Is the choke cable and throttle cables adjusted correctly? If so I would do the following.
Remove both carbs mark them for left and right,
Remove bowl confirm float level, proper jets pilot and main, ensure jets are clean and all passages are clean including the choke.
Check needle and needle jet make sure they are the right part numbers check for needle wear.
Double check the needle and seat for proper function make sure there is nothing stuck in one. Small piece of dirt or a hair will cause them to flood.
I use a torch tip cleaner for cleaning jets along with compressed air. Make sure you don't make the jet larger with the cleaner as they are brass / soft.
Other things to check are:
fuel filter and or tank screen,
compression,
belt is it the right length / width,
primary clutch for wear, broken springs, seized rollers etc,
secondary clutch for proper movement,
exhaust may be plugged mice packing away seeds,
another thing to check would be reeds but i don't think Polaris used them on that model in 95 but i'm not sure.
Good luck let me know what you find.