In case anyone finds this thread while googling or whatever, this is how things turned out:

After seeing three different podiatrists, I chose the one who had the least drastic, invasive approach. He anesthetized the toe with three local injections into the toe itself, and then removed just enough nail to get rid of the ingrown part. The toe's huge granuloma (a growth of bloody tissue caused by the irritation) would, he said, probably subside by itself, but he suggested I speed it along by soaking it in warm water or putting a warm wet teabag on top of it.

There was a bit of a reaction but nothing catastrophic or lasting. The main concern now, 4 months later, is that the toenail is regrowing in a weird and ugly fashion, although its unclear whether this will have any negative repercussions.