Well, I managed to uncover my old diningroom chairs from the basement, sorted out the best of the four, and brought it upstairs ....
- The good news:  It doesn't have protruding nails and doesn't hurt to sit on.
- The bad news:  It's about four inches too short to be comfortable as a desk chair.  Right now, I'm actually amazed I ever found them comfortable as dining chairs, but I have to temper that with the recognition that I have about two inches1 of orthotic insoles in my sneakers that I didn't need when I bought them.
Still, it's a small improvement for now.  I think.  I think we may end up getting rid of these chairs in the end rather than replacing the seat upholstery foam, though.  Which is a shame, because I really love the fabric ... it reminds me of one of the more luxurious Japanese haori I have, the one with the embroidered clouds in gold, silver and shakudo.2
1  Yes, I said about two inches.  No, it wasn't a typo.  That's how much heel lift it takes to make it possible for me to walk in a manner approaching normal with my screwed-up left foot.
2  Shakudo is a distinctively-colored alloy of gold and copper.  Yes, we're talking conspicuous consumption here.  Only the Samurai class were permitted to use it.