I can change between the large chainring and the medium one without issue, but the front derailleur that came with my road bike can't go low enough to shift to the small chainring. I tried to change derailleurs when I changed cranksets, but I can't without a chain tool, and I haven't (yet) had time to go get one.
Anyway, as per the subject line of my original post, I intend to get some sort of tool kit and mount it permanently on my road bike. Probably it'll just be a plastic tub in a water bottle bracket.