I want to project a photograph of an object on a much larger screen so that it can be manually traced on the screen. The problem is, using a D3 at 12mp, when the projection gets large enough (~6 feet/2 meters) in the long dimension, the edges become obscure. They're clear enough when you stand back, but if you're right on the screen, trying to follow an edge with a pencil, an edge may be a quarter-inch wide. I don't believe that changing to a higher resolution camera would help, because the resolution here is dependent on the resolution of the LCD in the projector, correct? Is it possible to break the image into several pieces and project them separately, essentially doing a kind of manual "stitch?" While you still run into some edge problems when projecting at more than 100%, they wouldn't be as severe as just projecting a whole frame at the LCD resolution, would they?
As others have pointed out, the resolution you get from a projector is fairly low compared to what you get from your D3.
If you have a reasonably affordable projector, or even a moderately expensive one, the best you can hope for in a 3:2 frame is 1620 x 1080 pixels with a "full HD" capable projector.
1620 pixels over 6 feet => 22.5 PPI
If you don't have a "full HD" capable projector, but merely one that agrees with 720p/i, your display will suffer even more.
1280 x 800 projector => 1200 pixels => 16.7 PPI
Since you want to avoid adjusting your projection size and viewing distance, you're left with adjusting the projection resolution.
As mentioned by others, stitching several projections is fiddly work at best, and you'll have a nightmarish job aligning the focus properly for four or more projectors. It may work for operation centers and suchlike, but I doubt that it will work well for art.
The alternative is to purchase or rent a more expensive projector, specifically one that is capable of displaying 4K (number of vertical lines, or horizontal resolution; 2K and "full HD" are very close); this will double your resolution to 45-50 PPI, and comes reasonably close (7-8.5 megapixels) to your native resolution.
Both JVC and Sony make such projectors (the quite expensive SXRD series
can be had, JVC's better-resolving DLA-SH4K
is about to get there), and I'm sure that there are competitors.
JVC has created an 8K (8192 x 4320) LCD projector chip, yielding more resolution than you or 1Ds MkIII, A900, and D3x owners need for single-shot images.
I'm beginning to think that I should just find a digital-to-slide film service and project a film slide...
That is certainly an option, provided that you can get a service that will provide you with the necessary resolution and quality. It's probably significantly cheaper than purchasing a 4K projector.