Christopher Weeks wrote:...top them off with sugar-water to replace the solids...
Leave out this step. Often adding more fermentables in the secondary can lead to off flavors because it stresses the yeast, which have already gone through this phase of their life cycle. (You can do this to incrementally increase the alcohol content as successive generations of yeast become more alcohol tolerant, maybe up to 20-25% ABV with a robust yeast, but it makes for a harsh brew.) Just leave the extra air space, and don't worry about it, and let it sit absolutely still under an airlock until you want to bottle it.
Even with strong commercial yeast I let things ferment "open," meaning a carboy cover with foil for air exchange for 2-3 days....but after this put an airlock on it, or you'll eventually get vinegar. The yeasts only need oxygen right at the beginning for multiplying their numbers in the wine, which apparently involves aerobic metabolism. After this it's anaerobic. When you rack to a secondary fermentor, this gives them a little more oxygen to use, and you might see a boost in activity again for a short while.
With wild yeasts, wait to put the airlock on until obvious signs of fermentation...hopefully no more than 4-5 days, after which point I'd pitch a commercial "killer" yeast strain to try to save it from turning into some other kind of ferment (vinegar or nail polish).
BUT the three one-gallon, side-by-side experiment is a good one to do. I once did this with 9 gallons of mead in one-gallon jugs. You can learn a lot this way.