Chicken – How much protein from the stock of one large chicken (2kg) carcass once legs, breasts and wings removed

In terms of commercial food processing, there are more efficient ways to extract gelatin than slow-simmering the bones, generally by treating the organic matter with a strong acid prior to boiling, then using commercial evaporation and filtering equipment which is far more efficient than anything a home or even restaurant cook has access to.

According to Gelatin Food Science (see the "Gelatin Manufacture" section) it can also be first treated with a strong base solution before acidifying it, which lowers the isoionic point. It's kind of difficult to explain exactly what that is if you don't have a background in organic chemistry; technically speaking it's a relationship between pH and electrical charge - but applied to extraction it refers to the pH at which the solubility of a protein (such as gelatin) is the lowest. Lowering this is a good thing in extraction, because it means that the gelatin will be easier to filter out in an acidic solution.

Thus I have to point out the question is actually a bit contradictory; if your goal is the extraction of gelatin then you want to decrease the solubility.

But I think this is all going to be beside the point anyway, because none of this applies to stock making; the goal in food processing is to extract the pure gelatin, not to get a flavourful stock. When making a stock you definitely don't want to use an acid solution, it's going to ruin the flavour.

Realistically, when it comes to stock-making, especially at home, the only way you're going to be able to extract more gelatin is to simmer it longer. That's it. When the bones break without any resistance, that means you've denatured all the collagen and you've got all the gelatin you're going to get. I wouldn't worry about solubility because typically in stock-making you're already using more than enough water to dissolve all the gelatin that you could possibly hope to extract.

If your quartering of the chicken was done quickly then you are just asking how long you can keep a chicken in the fridge.

How long will uncooked chicken keep in the fridge?

Your 40 hours is fine.