Out of your budget but for that screen and screen size a sim2 m120 or m150 would probably be the best 3d image you can get. 2 sales ive seen revently were 2500 with 11k hours and 3500 for 600 hours. Theyre limited to around 600 lumens, the person with 11k hours reported 550 lumens so they lose very little light output over time.
The dmd, lens, and rgb leds provide incredible dimensionality with just 2d content, for 3d it should be the best.
Also probably a bit high but something to keep an eye on is a runco d73d. Same dmd and leds, not quite as nice of lenses though. The stack will do around 800-900 lumens.
A Wolf Cinema SDC-18 or Optoma HD91 are rgb led with the 0.67" dmd and around 600 lumens.
The Panasonic PT-RZ470 or 475 is an rgb led/laser hybrid that should hit around 900 lumens calibrated.
I suggest the rgb led dlp projectors because they have the best motion performance.
Could be prudent to keep an eye out for 3chip dlp as theyre much brighter, as well as ultra bright dci projectors, though those will caution high power usage, heat output, and fan noise.
Ah... runco ls12, lumis 3d... more expensive though... 2-3k
Next I would focus on high brightness and single chip dlp
Hard to find but Barco/PD F35 AS3d or Digital Projection dVision 35 3d's will provide a bright sharp 3d image.
Though the may not support frame packing...
The Viewosnic LS750 and 850 are very bright dlp color wheel laser projectors. This is a good option due to the high brightness but lower power usage and heat output due to the lasers efficiency.
If youre not after the least crosstalk and smoothest motion, consider old JVC projectors starting with the x500 for best contrast 3d, try to avoid older than that due to brightness