As a homebrewer who has played quite a bit with yeast, this interests me.
I like the idea of using champagne yeast, as it does have some serious alcohol tolerance, and is available in dry form making it cheaper than many other brewers yeasts (I often use liquid specialty yeasts at $6-8 per dose.. ouch). That said, it is still a lot more expensive than buying a jar of bread yeast at the grocery store.
As for "mineral feed", there are a couple of common "yeast nutrient" mixes used.
Most center around the fact that brewers want the yeast to multiply early on in order to ferment faster (results in a cleaner flavor). In theory for DIY CO2 production, you want long and slow, not fast and furious.
Nitrogen is often supplemented before fermentation in non-grain based media (Barley generally has plenty, but honey does not), usually in the form of diammonium phosphate (aka DAP) and or food-grade urea. Oxygen is generally introduced as well, usually just by aeration. Both of these aid reproduction.
Some other mixes are meant to "energize" yeast after it has been going and gets into a "stuck ferment". These mostly consist of some DAP, with B vitamins, magnesium sulfate (epsom salt) and broken-down dead yeast added for micronutrients. These are usually added in fairly small quantities (1/4 tsp per gallon of liquid).
These would probably be helpful, but the expense of these products probably isn't worthwhile for DIY co2. Adding new water/sugar/yeast will replenish the little bit of needed mineral content, probably for less money. At the size of a part-full 2-liter bottle, maybe a grain or two of epsom salt might help out, particularly if your water is soft, and is certainly cheap enough...