I described this problem over on the Fear the Boot forums and immediately got a great answer. Runester of "Postcards from the Dungeon" fame recommended Mongoose as a solution. Mongoose is a free Google open source project. It provides a very lightweight web server. You just fire up the mongoose-3.0.exe executable in the directory you want to share, and it is immediately published on your local WiFi network as http://localhost:8080 or http://ip_address:8080. Mongoose also provides single-click start/stop service, so it's extremely handy. I can now hammer code on my laptop, hit refresh on my iPad, and instantly see my code updates.
I had already planned on buying an Apple Airport for my secure home network and streaming stereo solution. I wouldn't want to run a web server from my laptop while it's connected to the Internet, but since I already have a separate WiFi router for that, I'll just leave my Airport detached as a purely local loop.