Zach started digging into it around 15:00 while I went to pick up some tools, an acid to run through the pipes, and spare sail cloth and thread.
When I got back at 18:00, I saw a 1.5 inch diameter pipe, 3 feet long, packed solid through the entire length with partially dried up black water, calcium deposits, and God knows what else. Backwash from the holding tank and from our use of the head (before we realized it was clogged and we were just compacting the **** already in the pipes) was being held back without much success by tape and trash bags. We only had 3 latex gloves left and two of them were already on Zach's hands. And those were already torn. And we still didn't have the tools we needed to get the rest of the pipes and fittings off, which so happened to be equally clogged as the 3 foot pipe we were able to remove.
Thanks to the attitude of the cruising community to help each other out, we were able to find another boat on the docks that lent us a heat gun and the tools we needed. Unfortunately the *******s wouldn't come back and finish the entire job for us.
We removed every pipe and fitting related to the head, soaked it in a tub of bleach/water, broke our fishing pole to use as a rod to clear out the pipes, and man-handled everything back into place by no earlier than 22:00.
Our hands, including the old cuts that seem to never heal while on a boat as well as the new cuts received by trying to remove plumbing fixtures that have corroded into a near permanent union, were covered with the most disgusting concoction I've ever had the displeasure of coming into contact with. If we both walk away from that without some type of infection, I will consider the abilities of the human body to fight off infection a miraculous feat of God.
But I guess that's a part of boating. Just like the bbq, beer, and sunsets.
Addendum: The head still isn't working. I'm guessing the high pressure we created trying to force a solid through a solid has messed up our rubber seals. It's an older model head and we couldn't find replacement seals at any of the shops around here, so we bought an entirely new head for $140 and plan on replacing it this evening.