So, it's been five days since I pulled out the poison ivy. I have a few more lessons learned.
1) Eat before you dig, if there's a big patch. You can't eat while you dig.
2) Make sure your gloves are rubber and puncture resistant, or that you have rubber gloves under garden gloves. Either way, don't let the sap get through the glove.
3) Make sure your gloves protect your forearms, since sleeves can ride up.
4) Don't put your face near the plant or your clothes. Don't rest your chin on your knee. Don't wipe your face with your arms. Wash your face well, and be glad you remembered goggles.
5) If you like your clothes, wash them immediately or the sap will leave black marks.
As for the rash, I'm glad to say that since the end of the third day, no new itchy spots have appeared. I got a mild case, though it is in a few places, including the palm of my hand and my chin. By today (day 5), most of the itching has passed, but the blemishes remain.
As for the poison ivy, no new growth can be seen...