The RS10 is a great projector for . . . movies. For "sharpness" and motion, I would look towards DLP I think, however I can't narrow it down from there. Some brands I would look at are Mitsubishi, BenQ, and Optoma, for instance (maybe even in that order, but only due to very topical impressions; further research is needed on my behalf). This is coming from a JVC owner, btw.
So, how could it be that JVC doesn't look as "sharp" or be as good with motion, yet is considered a great movie projector? It's for the native contrast and black detail. The "look" provides a very filmic presentation. Things that are probably quite wasted on you if this is for SPORTS and VIDEO GAMES. There are a few people that have serious issue with how JVC handles motion. There isn't any frame interpolation either, something that I would never use, but I'm not sure if you can get that on a DLP (but for sure on 3LCD).
The JVC has a very high fill, and it's rather difficult to notice pixelation. At the same time, having more distinguishable pixels is what makes something look more "sharp", if you will.
The main issue with DLP is that most typically the shift and zoom flexibilities are very limited compared to either LCD or LCOS (however one model did come out recently that actually had pretty decent flexibility, can't remember what it was though). You can find certain zoom calculators at vendor's sites, to see if your placement can allow the ideal size, and also if it can shoot the pic low enough, etc. OTOH, DLPs are typically quite bright. I imagine they make more noise due to their particular technology, but hopefully that is not the case, or only minimally so.
As for the RBE, rainbow effect, it's said that not even 1% of the population can detect it. Not only that, I've been led to believe that this number is continually reduced due to improving technology; better color wheels, that also spin faster.
EDIT: another thought why DLP could be tough is that it's not just for video games... but for the Wii. That means standing up and moving, therefore dictating a high projector placement, which may be tough with DLP. The PJ will basically need to be above you for sure, maybe even in front of you, depending, which means a very large vertical shift. Try the Epson from your friend I think in this case.
