How much citric acid should I use to preserve mayonnaise on a cups/ml ratio?

First, don't make assumptions based on other recipes. Food safety is so complicated, not even the specialists try to predict anything. They test recipes empirically until they have found ones that work. Of course they take guesses at what is likely to work, but they only know after they've made and measured it.

Luckily, people have tested recipes for longer life mayonnaise. The result is that you have to use 1 gram of acid and 15 g of water per yolk. You also have to pasteurize the yolks, which means that you need to get them above 65 Celsius during the mayonnaise making stage. The curdling temperature of yolks is changed by the acidity and the speed of heating, with this ratio, it occurs somewhere between 82 and 88 Celsius. So you really have to be very accurate when producing the longer-shelf-life mayonnaise, using both a thermometer and a high-sensitivity scale (don't measure by volume!). I suggest reading the whole document on safe mayonnaise making here, it is quite informative.

Your idea for "large batches to get me through the winter" probably still won't work, though. First, I wouldn't keep this mayonnaise indefinitely long. It only gives you a 5D reduction for salmonella, and of course you still get bacterial contamination of other species after the mayo is made. They may be slow to grow with all the acid and in the fridge temperature, but they still grow. Also you have mold and plain old quality problems such as rancidity and lactic fermentation. The authors of that article only confirmed the safety for 4 weeks.

Second, you can't be scaling the recipe indefinitely to make one large batch. As you saw above, you need a very tight temperature control. If you were to dump a dozen of yolks into the bowl, and then add 12 cups of oil, no burner will be able to maintain constant temperature throughout the emulsion, especially once you have enough air in it that conduction slows down. 3 yolks are normal for a batch, up to 5 can be done well, above that it becomes quite difficult.

Third, you might find out that you simply don't like it. This mayonnaise should have a pH of 3.5 or below. This is not yet pickle-taste territory, but it's still very sour. If you don't enjoy mayonnaise which tastes of citric acid foremost, you might find out that you don't want to do acid preservation.