Almond Milk for cow's milk was a really common substitution in medieval recipes. A lot of medieval recipes used almond milk - almonds being a lot easier to store without spoiling and find reliably when a medieval cook needed some.
Almond milk was a staple of the medieval kitchen. It was used in a wide variety of dishes as a substitute for milk or cream, especially on "fish days", when the church placed restrictions on what foods could be eaten (the most prominent of which were the days during lent).
from http://www.medievalcookery.com/recipes/almondmilk.html
In the Middle Ages, animal milk was, of course, not refrigerated, and fresh milk did not stay fresh for long. Most cooks simply did not use much milk as the short shelf-life of the product made it a difficult ingredient to depend upon... Rather than animal milk, Medieval cooks turned to something they could depend upon, and that was the milky liquid produced by grinding almonds or walnuts. This liquid, high in natural fats, could be prepared fresh whenever needed in whatever quantities. It also could be made well ahead of time and stored with no danger of degeneration. Because of its high fat content, it, like animal milk, could be churned into butter, and because it was not animal milk, it could be used and consumed during Church designated meatless days.
from http://godecookery.com/goderec/grec31.htm
Some dishes cannot be made with this substitution, those that depend on the physical and chemical properties of milk - like cheese, or whipped cream. It would take a lot of processing and additives to make the almond milk mimic those products. However, both milks contain fats, proteins, and sugars in solution, and so behave similarly enough in the chemistry of cooking to make them easy substitutes.
I will admit that while I cited medievalcookery.com and godecookery.com because the quotes were convenient, I posted my comment originally drawing from David Freedman and Elizabeth Cook's "How to Milk an Almond, Stuff and Egg, and Armor a Turnip: A thousand years of recipes" which is very well researched and contains a number of period citations and recipes.
In the US, most almonds are already pasteurized, even when they are listed as "raw". One of the methods is to steam blast the nuts, which heats up the outside of the almond to 205°F (96°C). However, this process is mostly done because of Salmonella concerns, rather than the yeasts and microbes that cause the souring of the milk. You could do something similar by blanching the nuts in boiling water for a few seconds before you soak them.
You could also try soaking the almonds for even less time, I've found that 12 hours or overnight will do the trick, rather than the 2 days you mentioned.
Some producers of almond milk also "ultra-pasteurize" the liquid by heating it to a temperature of 280°F (138°C) and cooling it down quickly before packaging but getting to that temperature is hard to accomplish in a home kitchen. You could try heating to 162°F (72°C) for 15 seconds after you've collected all the liquid, though be sure to have a plan to cool the milk down quickly afterwards.
Exposure to oxygen, yeasts and microbes are predominately what causes the spoiling. The oxygen can rancid the fats in almonds, molds can grown on the surface, yeasts can start to ferment the liquid, and other spoiling.
Best Answer
I think that both will do the purpose you are looking for. The soaking is more to bring the nutrients out of the almond before preparing the dish you need them for or in this case the milk. I would try just the soaking once and if you want it more sweet then bitter add the sugar into the water you are soaking it in, this might neutralize the bitterness in the milk when it is ready to drink. Also to neutralize the bitterness try adding vanilla extract or even cinnamon if you would like that.