Thanks again for the feedback, everyone. I'm not sure what the specs are of my DMM; it's one of the cheapest ones I could buy. I wish I had access to an o'scope, but, alas, I do not (at least not within an hour's drive of here).
I appreciate all the alternatives to my straight 24VAC->5VDC conversion, but I'm going to try to build this with what I've got on-hand. I actually used my last 7805 for another project today, so I'll have to make do with an LM317 and a heat sink. If the heat proves to be too much to adequately sink away from the voltage regulator, I'll have to consider another solution, but this is part of the discovery process. Given that I do have multiple LM317 VRs, I could try doing a multi-step stepdown...
Oh, and George, that's a pretty interesting networking protocol you've got going there. I'm going to have to give that a good going-over. This project was spawned from the desire to get some grass to grow where my dogs have decimated the yard of my rental house; I had a very dumb timer that I used two years ago; it could only do intervals from "now", so there was no way to program it for 4am without actually getting up at 4am. ;D I disassembled that a while ago, with the intention of making it smart, but decided that I was getting held up by the space constraints and voltage differences (it ran off 3V) and decided to start from scratch with commodity hardware. So far, I've got about $45-50 into two valves, PVC tubing, and fittings. The brass fittings to convert the PVC to garden hose thread cost nearly as much as one of the valves. But it's still (ever so slightly) cheaper than buying a 2-zone programmable sprinkler controller.
Be careful using the LM317's in that the case is connected to Vout rather than ground like the 78xx series. You need to be careful how you heatsink them because an uninsulated sink will be "hot" with your output voltage. This makes using them in a multi-stepdown configuration difficult.
I wish I had access to an o'scope, but, alas, I do not (at least not within an hour's drive of here).