We eventually got a handyman in our ward to look at it with me to get an opinion if we should cut into the ceiling and where, and turns out he has a son that is a plumber in Portland. He said plumbing calls have dried up and they have very little work currently, so we were able to get him and his son to come help with the drain at a seriously discounted rate.
Turns out that a drain pipe had become disconnected at a 90 degree joint, then the leaking water was above and leaked into the heating ducts, which made it very difficult to pin-point the leak. We had to demolish several parts of the garage ceiling and wall board, and a large chuck of the same in the basement hallway.
The traps and pipes under the kitchen sink and island (which we have had trouble with since moving in) had been installed with sub-code (in fact illegal) piping, which we completely replaced with new stuff in code. It no longer leaks and is a lot sturdier. In additional to the break, there was also still a plug in the drain, which required renting a 50' snake from home depot (another 20' beyond the one I bought for the job). This did the trick, and we also installed a cleanout access point in the basement pipe to make snaking out the drain easier in the future. I learned lots about heating vents, plumbing, and even water heaters (who knew they had two heating elements and two thermostats the have to be kept in sync to heat water efficiently). I have previously adjusted up only one of these on each of the water heaters. Now we have increased the temp to 140 degrees on both, and seem to have enough hot water now to last several showers (an important feature on Sunday morning when all want to shower near the same time).