I had an XRS and when I was done with it, there were very few sleds that could touch it. Even XP's.
First thing i did was get rid of the hellish powderlite track and went with a 2006 summit X powdermax track (stock)... you can get one from tracks canada or tracks usa, the camo version is not ported and the ports don't matter too much..you can add them if you want. tracks canada is pretty good price. mine was a 159. sold my old track and net cost was only a few hun.
That was a huge increase in performance...i think more than what a big bore would get you....yes it's that much (when clutched properly).
Secondly get a proper clutch kit and get it dailed 100%. Dj's kit is spot on for the XRS. This is another huge improvement....do this even if you don't change the track as it's an easy install and reasonable cash.
Third get a 14:1 head as the stock head on the 2007 800R sucks. Stock is really low compression and less than even a 2006 800 summit X!!! Also it will broaden the power curve allowing for easier tuning and a much funner sled. I went with SLP on mine, but now running Terra Alps and RKT, and like those two way more than the SLP.
After that all i did was the small things like remove all foam, set oil injection properly (not stock as the dealers set them way way too high, measure and adjust consumption several times is the only way to do it right). I added some mesh to the vents to keep from ingesting powder.
That XRS has an amazing shock package, i wish i could get my hands on a set of XRS shocks!!!! I really loved that sled (after dealer replaced the first engine that failed in it)...but perfomance wise it was just amazingly quick in the mtns.