Sorrry for the delayed response Eric.
Shallow minimally dug holes or trenches, just enough to cover the sets or potato roots will work. Yes cover the onion sets and sweet potato roots with soil, but don't put all the woodchips back in place, untill your plants get big enough. 6" of chips has
alot of smothering power, and you'll want to make sure those plants can get light quickly. Maybe taper the woodchips so its not more then 2" thick where the plants are; then as the plants get bigger, you can tuck the woodchips back around them. Your woodchips will just be thicker around your holes or trenches untill the chips can all get moved back. Your plants
should grow quickly enough, so maybe after a few weeks you can move the chips back. The vines are pretty tough, its the onions growing crown you definitely don't want to bury, so make sure you keep the onions leaves above the chip line. If the onions have a short neck, as the leaves age and fall off, the stem/neck will get longer allowing you to move more chips back.
Outside sources of fertility are great, just set up sufficient composting strategies to minimize efforts in composting. Windrows are great for composting, or
pallets tied together make great
compost bins you can mover from season to season. You set up the bins where you'll need the compost to minimize labor. You can also use those pallet compost bins as a giant raised bed for planting things like sweet potatoes or potatoes. So you can compost all winter long, plant in the bins in spring, and spread the compost in fall at harvest. The slats in the sides, plus the open top are all places to plant, then after your crop is done, you untie the pallets, and the compost gets spread while collecting your root crop.
Any material you can get without to much effort is good. Cardbord works great as a temporary weed barrier and mulch. Any horse barns that will load a truck or trailer with manure is another option.
Local Arborist and utility companies or their line clearance contractors are often great sources for free woodchips delivered, when they're working in your area.
Hope that helps!