I have Aqua Lite's from VIVOBAREFOOT that I have worn in tons of situations from offices to snow (the blue ones are waterproof). They're flat on bottom and mostly flat on top. I've never kicked in them but they seem like they might work.

Anyone else agree?

If you have strong feet, try Sockwa

A couple others I would consider are ZEMgear and Sole Runner (you can buy one Sole Runner model on Amazon, the rest have to be ordered from Europe). The Sole Runners have a super thin sole similar in thickness to the the Aapa and the Sockwa.

Have you checked out Sockwa?

I think they would be perfect for what you are looking for. I would recommend the G collection for work and for your martial arts. They have a lycra/neoprene upper with a thin 1.2mm TPU sole. It is as if you are wearing nothing at all. You could also take another route and try out the brand new, X8, which is designed just like the G; however, instead of the lycra/neoprene upper, there is a 3 layer ariaprene mesh to allow for extreme breath-ability, if you tend to have perspiring feet. They both have wide toe boxes with no laces, making it easy to slip on and off.

Check out our website to see more: http://www.sockwa.com

I wear Lems during the day, managing a small retail store. They fit your description to the t. For me the advantage is that I can wash them once a week because I do not wear socks.