I think you may want to try on different models on some of these shoes, since they do vary. New Balance, for example, have some sneaker models I hated, but also had one that beat out all the others for me when I replaced my sneakers a month or two ago. I also have a high arch, and some light plantar fasciatis, so I get how important the shoes are. If you want extremely firm support, Birkenstocks might be something to try. I, personally don't like them - there are some design issues that don't fit my foot well - but if it works for you, it might be a great choice, and isn't as pricey as SAS. Vionic can be a mixed bag, but are worth trying. I definitely like one of their flip flop styles, and use it exclusively around the house, and even out and about in Summer.
Finally, Dansko might be another one to try. They're great for folks that have to be on their feet all day - nurses and chefs tend to use this brand a lot. Sometimes I have problems with where the toe hits on some their shoes, but they're really supportive. Good luck! I totally get how frustrating shoe shopping can be.