Thanks for all the replies. I don't have any trouble with the paper/glue - I've been using contact cement and it sticks pretty good. I've tried it with regular photos, and postcard thickness prints. I glue it to the oversized plywood blank and then trim the edges to size.
But if I try to cut a puzzle with the picture facing up, I have no way to sketch a pattern and I do need a pattern - I'd like the pieces to look at least something like a real jigsaw piece and without a pattern I can't seem to visualize it and I end up with a bunch of funky shapes that just barely interlock.
If I cut them with the photo facing down I can sketch out a pattern on the bottom, but then it ends up getting fine scratches on the paper from all the turning, and fuzzies from the blade.
I bought a roll of that low-tack clear film from hobby lobby but haven't tried to cut a sheet and print a pattern on it yet. I might try that, worst that happens is that I destroy the printer when it jams.
I am happy with the technique of cutting the blank in half, and then each half in half and continuing that way until they're down to a decent size. They all end up roughly the same size that way.
My saw is the Dewalt. It's no Excaliber, but it's not a $2 garage sale toy either so I'm assuming most of my problems are operator error.