As a long time grower of sweet potatoes in several regions, I can vouch for not letting the vines root along their length, unless perhaps you are in so tropical a climate as to have them basically become a perennial groundcover, and even there, finding the largest roots to harvest would still be a challenge. Raised beds and mulching help with this, but in wet weather roots will grow down through mulch, and then going along the rows and lifting the vines and setting them back down helps, and/or stuffing coarse mulch, bundles of sticks, etc. up under there as well.
Not letting the leaves droop from drought is also important. In fact this is good for just about every kind of vegetable. When I was growing for high-value organic markets I was taught that if you see foliage droop on anything, even if it recovers overnight, you are losing yield and quality. Although yes, in a homestead situation resilience is also important, and you will still get a yield in spite of this. A long drought followed by heavy rain can also make roots split.
Most important of all, though, is to work toward what I call a "fluffy" soil....this goes for carrots as well. Neither likes a heavy clay and it will lead to small twisty roots on both. Sandy soil is ideal, good loam is good too. If you have clay the answer is finely divided organic matter incorporated in. I used to make this by running a mower over dry leaves, grass, etc. in the pathways between those beds allocated to these crops, and then dig and/or till this into the beds themselves...up to an inch or two depth of "powder" per year. A bit of urine helps counteract the nitrogen uptake issue with this kind of organic matter use, but fortunately neither sweets nor carrots like a lot of N anyway.