The Epson 3100/3700 improved the contrast considerably over they 3000/3500 it replaced. These were on sale for $800 recently new but I believe only the refurbished are in that price range now. If you can find any of the older BenQ models like the w1060, HT1070 or the 2050 used should be priced at or below your budget. ViewSonic pro7827hd was selling for $399 at on time for refurbished but most are gone but look around as some might still be around.
"Smart enough to know better, to old to care" ------ Dedicated Bat Cave Home Theater, JVC RS49U/Mitsubishi HC7900DW Projector, 110" 16:9 Jamestown screen with variable power masking for CIW 2.50:1 to 16:9, Marantz 7009 with 7.1.4 Atmos with Ohm mains,3 DIY Subs (2 15" (1 ported, 1 sealed and a 12" 4th order bandpass), 1 DIY butt kicker, Custom Built HTPC, 18TB DroboFS NAS