Before you go out and spend all that hard earned money on electric start, try turning the gas off when you park the sled or park it going up hill. Front end elevated.
Could be bad needle and seats in the carbs. I have the same sled and never had a problem starting it and I have not replaced the needle and seats in the carbs. I'll even run mine for a couple of minutes at the end of the day with the gas turned off. I know the needle and seats are leaking because if I don't follow this proceedure, it floods and then I wish I had electric start.
On the other hand, electric start kits are fairly expensive. $500+ I think from the dealer. And you may also need a different clutch to accept the starter ring.
Someone else can hopefully chime in with that info for you.
D