With a budget like that you've got a fair amount of options because you're both past the $2000 contrast gap AND well into the price-point where a majority will make your required throw distance or at least be very close.
The best movie-only projector will have you looking at the top of your budget for a deal on a JVC. The JVC (even many older models) has a black-level that STILL can't be touched by anything else.
Below that but still at or above budget is probably the Sony hw55 with both solid blacks and a good iris.
More comfortably within your budget in the $2000-2500 range are the Panasonic ae8000, Epson 5030ub and Sony hw40. The Sony is LCoS and the Epson/Panasonic are both high-performing LCD and all three have fairly similar measured contrast though the Sony doesn't use (nor have) an iris.
The hw40 is usually the top recommendation for its price segment, but a JVC will be in its own league if you can stretch the budget or find a good sale.
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Last edited by Ftoast; 08-24-2014 at 08:26 PM.