The experimental solution we tried out last week for the paths in our vegetable garden proves to have a few flaws. For one thing, a couple of days of heavy rain turned the dirt paths to mud paths, which aren't exactly the a nice stable surface for walking on. It also weakened the kraft-paper underlayment to the point that a couple of ambitious weeds were able to poke their way clean through the paper and the dirt above it, which kind of defeats the purpose of putting down the barrier in the first place.
For the time being, we've covered up the mud with a layer of leaves, which we had been using to mulch the garden beds during the winter and raked off the top as we prepared the beds for planting. The path is still a bit squishy underfoot, but at least it's not slippery. But for the long term, it appears that dirt over paper is not an ideal solution for the garden paths. However, paper with something else on top, like wood chips, could still prove a viable solution. Although having a whole truckload of woodchips delivered to our house appears to be impractical, I did recently come across some information I'd dug up last year and then forgotten about a tree service in a nearby town (about 7 miles) that will let you come to their yard "by appointment" and haul your own wood chips for free. (You can also get logs from them, which we don't happen to need, but I'm planning to pass the information on to a friend who has a fireplace.)
So my current thinking is, we pick up some of those big paper lawn and leaf bags, and we haul them to the tree service and fill them with wood chips. Well, actually, when I say "we," I probably mean "I," because they're only open on weekdays while Brian is at work. But in any case, I fill up several bags with wood chips—as many as I can easily stuff into the back of our little Fit—haul them home, and drag them down to the garden. Then, I can just lay the entire bag down in the path, slit it open the top, and either tuck under the top layer of paper or cut it up entirely. No need to mess with cutting kraft paper off the roll first and laying it out; the bag itself will provide a ready-made weed barrier, with the wood chips laid out on top.
Of course, the downside of this is that it wouldn't use up all that leftover kraft paper we have from our paper floor project, and we would have to pay something for the bags. But at 50 cents a bag or whatever, with no additional charge for the wood chips, it's probably the most cost-effective idea we've come up with so far.