UPDATE from me, the OP.
Today I picked up a nice clamping magnifying desk lamp at everyone's favorite craft shop -- Harbor Freight.
It's not a floor-stander, but it has a much longer arm than the little desk lamp I already have.
It has fluorescent, rather than LED lighting, which is a bit of a shame. The light is daylight quality, though, and the color rendition is awesome.
The bright side of the fluorescent light is that it's replaceable, which is seldom true with the LED magnifying lamps I've seen.
It also has a cover, so I don't have to worry about sunbeams coming through the window then shining through the lamp and creating a fire. Yes that's a problem people have talked about and shown pictures in reviews. Oh the fond memories of starting little fires with tiny magnifying glasses as a child, ha-ha.
Anyway, thanks everyone for the ideas. They were all very helpful.