I started off with an old fan sled and similar questions. I ended up with a 600 RMK as my primary sled, but I've got another Indy Trail I'm working on building into an ultralight mod sled. Merlin covered a lot of ground, but I'll throw in my two cents.
First, I'd recommend saving your money on horsepower upgrades for now. You can make more power out of a fan sled, but only the 3-5 HP you can get from careful tuning is remotely cost-effective compared to upgrading to a liquid-cooled sled. There is more power to be made from exhaust, porting, bigger carbs, and so on, but that takes a lot of time, effort, and know-how. Beyond that, most people don't bother is because you've got heat issues when you try to push more power with a fan. It's a dead horse that gets beaten every time someone posts about a fan sled, but I bring it up for the sake of expectations.
You hit on easily the biggest thing you can do, which is lose unnecessary weight. Ditch any mirrors, luggage rack, and such add-ons. If you're willing to do some adapting and fabricating, you could fit a lightweight seat from any number of sleds (doesn't have to be Polaris); you might find something cheap perusing Craigslist. The other thing to look for is a set of plastic skis; those shed significant weight and typically perform better. They're not universal though, so make sure you know how you're going to fit them before you buy. Pretty sure you've got a longer track on that, so with some weight-shedding you should be able to manage off-trail if it's not too deep.