NO! Do not attempt to modify your natural draw length. I tried it and it turned into a chain of events that started shooting problems that I still haven't recovered from, 15 years on.

About the loop, your draw length does not change. Period. However, using a longer loop will allow you to shoot a shorter draw length bow. I've shot 2" long loops in order to shoot a 31" bow. Now, that's an extreme example and I do not recommend going that far. The main reason is it takes your peep sight a long way from your eye. The string angle with these squatty little bows they're making nowadays moves the peep forward to start with, then adding another inch or two to that.... You have to have a peep the size of a hulahoop just to see thru it.

But for 'normal' usage of a string loop... Your own physical draw length never changes. You shorten the bow's draw length and/or adjust the release's length of pull to offset the length of the loop.

Really and truly though, at 31" draw you are not going to have much problem getting a bow. A few models do not go past 30" draw but the vast majority of bows are made to 31". When you get over 32" is when you begin having problems. At my 33 1/2" draw length, there are very few bows made to accomodate it.

I like the specs you're looking for in a bow. For the most part. But here you are saying on the one hand that you're having trouble finding a bow and then, on the other hand, you're getting all picky and specifying single cam only. Fine and dandy if a single is what you really want, but don't rule out dual cam bows entirely until you give one a try.

I have a strong perference for duals. In my experience, they are much easier to work with and require less maintenance and tuning than singles. With the possible exception of those singles that use a dual track idler and split that long string into two shorter sections.