Prevent cocoa from settling

You are fighting a losing battle here. Cocoa powder does not dissolve in water, and it will simply sediment over time. If you are unwilling to do something about viscosity (and I understand that - gums do change flavor), you can only slow the process by using methods which are increasingly difficult to apply at home (basically, creating smaller cocoa powder pieces).

If you are not already doing so, boiling the sauce first will help somewhat. This is the same line of thinking as adding some starch (cornstarch or tapioca were mentioned, doesn't matter which). Cocoa powder itself is mostly starch, so once it is cooked, it will be more puddinglike and will bind water better.

My preferred solution though would be to abandon the recipe and start working with chocolate instead. Chocolate is a sol, consisting of solid particles suspended in fat. Much like an emulsion, only both phases are solid. When you mix it with the fatty emulsion of milk, you achieve a much smoother mixture than the cocoa powder + water combination. It won't guarantee perfect dispersion, but should be better. Unlike the previous suggestion, do not boil or you will lose the advantages of the existing sol/emulsion.

One possibility might be to simply store the sauce as a powder (with the desired proportions of cocoa, sugar, perhaps milk powder). This would let you mix it either with water or milk, as you wished, for individual uses - and mixing an individual portion might not be as annoying as trying to remix a whole container every time.

Another possibility might be to store it as a paste - mixed with a minimal amount of water or milk, which can be thinned to the correct consistency when needed. This might be easier to mix than a powder (it might tend to clump), and so might be more convenient if you're making several batches in a short period of time.

You might also consider the means of storage - I was thinking such a sauce might not last too long in the fridge to begin with - since it doesn't have the preservative qualities, say, a syrup would have. But if you portioned it off and froze it, that would make it last longer - and getting back to the question, having the sauce mixed thoroughly just before freezing individual sized portions might mean it doesn't have time to settle too badly before it freezes, and so might not need too much mixing after thawing, especially if used promptly.

Another option might be a small quantity of corn starch and heating to activate - it usually doesn't add much flavor to my taste, especially if only using a bit (though tastes may differ) - even getting the sauce a little thicker might encourage the cocoa solids to stay in suspension rather than settle (I think this might be helped by using milk rather than water in the sauce, because it is just an emulsion and just a bit thicker).

Actually, since you didn't add your process - just heating the sauce might help (if you did not do so in the sauce-making process). Heating the cocoa solids should help melt the cocoa butter and disperse the solids. I'm only mentioning it because I could see a sauce made with those ingredients in a cold process, just mechanical mixing - heating may change the flavor, if you enjoyed the taste of the cold processed sauce, but it might be a good or bad change.

Along the same lines (and from the same source) the type of cocoa powder you use might make a difference (dutch cocoa is supposedly easier to dissolve). This will change the flavor - but it might be worth experimenting with.

Also, while I was looking things up I found this recipe for a chocolate syrup that offers a substitution of liquid stevia - which makes me think the sugar in this recipe isn't needed in this recipe for chemical or physical purposes. The syrup is made by heating chocolate and water (and the sugar or stevia, and a bit of vanilla extract), and it forms a thick sauce that dissolves far better than cocoa powder (in cold milk, for this particular recipe) and doesn't sound like it settles as badly. I'm not sure if the heating is the only difference, or if the vanilla extract might also play a role or what - but you might be able to make a syrup (via heating) with much less sugar than you think. And you can thin to taste either just before serving or before storing, whichever works best for you and settles the least.

And, finally, a moderate use of soy lecithin may help prevent settling (that recipe uses heating, and also using unsweetened chocolate aka cocoa liquor rather than cocoa powder may help, with the higher proportion of cocoa butter). Soy lecithin is often used in chocolate bars and the like, because it is an emulsifier and helps prevent settling - and it shouldn't have negative effects on the flavor when combined with chocolate, otherwise it wouldn't be so widely used. It can be certainly be purchased online, or it may be carried in some shops (especially those that carry bulk spices or raw ingredients).

I would inquire as to the best place to introduce "Tapioca Flour." It is a great thickener and can often used in many dessert applications.