I guess the best suggestion is to say: "sell the sidekick and get a samurai", there are not enough options to make your sidekick any better. The lift was just for looks, and the tire size was waaay to big for the vehicle! You should have left the vehicle stock height and maybe some 235/75/16's you would go plenty far off road. There was no reason to lift this ride!
A Samurai case does not just "bolt in", it will require a good deal of fab work for brackets and connecting to the trans.
Swapping in Toy axles is definitely not a bolt in, considering that you would have to use a Toy IFS or straight axle in the front, both would require a lot of custom fab work, unless there is a kit I haven't seen. Oh yeah there is the trailslayer kit, for the measly sum of $3000, not including the axles!!
Cold Air Intake, 2" exhaust, and headers are very good ideas.
Sure, going down a size when it's time to buy new tires is not a bad idea. This Sidekick already has 33's though, And since the owner metioned gears, swapping in a lower ring gear and pinion set is the best advice in my opinion. I do not know or pretend to know what ratio's are out there aftermarket, but there are 5.62's, when you can find them. And this would be a "stock" replacement.