When it comes to shoes I have the worst luck. I also need to have them tied down, I can no longer wear anything with an open back...they always feel like they will fall off. I miss my open back sandals...I lived in them through the months with no snow. I was a big Birk girl but I can't wear them any more...even the ones with the back strap I find the strap gets to loose.
However, concerning New Balance. I worked in an Athletic Shoe store for many years...and we worked with people with foot problems. New Balance is the real thing. They are a fantastic shoe company. Keep in mind like with any shoe company they have their low end and high end models. You need to spend a few extra bucks to get the good ones but it is worth it. New balance uses a very absorbent cushioning system called abzorb. To your touch it might not feel like the softest thing but is very absorbent . Plus if you need extra support they use the roll bar system that helps with that plus they make them in all sizes with narow and wide widths. I am a huge New Balance fan. Also, mad by New Balance is a company called Denham. These shoes are more in the casual area but they are good if you need something more dressy (a solid black leather shoe). Nothing very feminine but it is better than wearing running shoes with your dress clothes.
I'm going to check out some of these brands mentioned here because I am in need of new sandals...maybe I'll have some luck.