Okay, so I have too much work to focus on to experiment with this yet, so I thought I might outsource this to anyone interested who:
1) takes photos of their paintings often enough for this to be worthwhile to them, and
2) has a good handle on photography already and a decent camera.
Basically, I take decent photos of paintings with some caveats. For one thing, they're high-res but not super high-res, on account of not having a medium-format (or even a full-frame) camera. But that's not really an issue for us since the resolution we get is good enough for the web and then some.
But glare! Ugh! We really don't have a good solution for that. I don't mean the easily avoidable glare, but rather the little spots and streaks of glare where the brushstrokes left some texture in the paint. It's a big hassle for us, leaving us with images that aren't as good as they could be and creating work for us (getting rid of especially bad glare spots manually in Photoshop, altering perspective in Photoshop due to the slight angle I take photos at to minimize glare, etc).
So check this out: jmahorney.blogspot.com/2010/08/where-you-been-or-death-to-glare.html
If anyone wants to try that out properly and carefully and post their results, that would be awesome, but I'll try it eventually so only do it if you need to be able to take good photos of your work anyway. I'm sure it works to get rid of glare, but I want to try to find any problems this method creates before recommending it… and before telling Mark we need to buy new equipment!