I'm not sure how many holes you have to work with, but if there are enough I think that sheet metal screws would work. I see two problems with the self-tapping one you tried. First, a #10 was probably too small. And second, a self-tapping screw can cut a new thread on it's second use. That leaves very little metal between the original thread and the second one.
A sheet metal screw would be the choice. It will form the thread instead of cutting it. So it should follow the original thread on the second and subsequent uses. Electronic enclosures have used sheet metal screws for a long time and, with due care, they can be removed and reused many times. I would think with the diameter holes you have a 1/4" sheet metal screw could be used.
A tip on reusing a sheet metal screw: Since the thread is already formed, you should insert the screw with moderate force only until it contacts the metal surface. Then, with that moderate force, turn it backwards until it "clicks". Stop immediately and turn it forward to tighten it. This ensures that it will find the original thread and not create a new one. Of course, do not over-tighten it.
And yes, whatever you choose, do use stainless.