Usually it is the case that people with low arches do overpronate. Sometimes, however we find that a person might have developed quite an efficient running style despite their foot gait indicating that they should overpronate.
For example, I was working in one of the Sweatshops the other day, and was serving a customer who sounds very similar (it wasn't you was it?!). From just looking at his feet, he looked as if he needed a lot of support. When, however, he ran over the footscan, and when I watched him run, he looked as if he needed very little support at all - almost a neutral runner.
When deciding what shoes to recommend to him, I thought that he had relatively good running form. However I also took into account that his running form might well deteriorate slightly, when he got tired, because of the way that his foot leaned inwards and because of the height of his arches. So I thought that a stability shoe would be most appropriate, but not a full motion control shoe as this would have restricted his foot too much (too much support, and they have a very 'straight shape', he would have needed a more curved shoe to allow him to take advantage of the efficient style he had developed).
For yourself, I would suggest that you have a look at your old shoes, and see if they are inclined to lean inwards at all. If they do have a prominent lean inwards, then you need more support than that shoe gives you.
Also, regarding the cushioning, the cushioning in the Kayanos might be a bit too soft for you (believe it or not!). Heavier and taller runners would need a firmer, more responsive cushioning. This is because softer cushioning would compress too quickly at the point of impact and not cushion you completely. A firmer cushioning will not compress so quickly, so will give cushioning for the full impact on each step. Also it will last longer.
Without looking at your feet, it is pretty difficult to give good advice. In general, though, I think the conclusion that I am coming to is that you could stick with the kind of stability shoe that you have been using, but avoid too supportive shoes and motion control shoes. If you have a neutral/mildly pronating running style, then having a bit of extra support won't be terrible as long as the shoe doesn't give too much support. If the Kayano's haven't given you the cushioning you need, then maybe brands with a more firm and responsive cushioning such as Saucony, Adidas, New Balance, or Mizuno would be worth a try. I don't know much about Brooks but I think they have a reputation for being a good "big-guy" shoe as well.
anna