So: trigger alert for the squeamish. Some woundy-type details follow.
Now that I don't have to maintain constant pressure to keep the blood from making a mess everywhere I was able to take a long look at the affected area. I lost only part of the side of the nail, which apparently did what it's evolved to do and deflected the knife down along the side of the finger. The actual fingertip is mostly intact and the root of the nail is untouched. The "missing bit" is filling in nicely and there's no sign of infection or other hindrances to clean healing.
That means I can expect everything to come back in and be pretty much normal given enough time. I'm already able to type through the bandage without pain (or associated meds, apart from a wee dram or two) which is encouraging as Hell to me.
Whew. Lesson learned, you betcher good-natured donkey.