Well, probably the most expensive part of me doing the plate will be the shipping of it. The material I'm sure I could find pretty cheap. I may even be able to get it for free if I look hard enough. The thickest stuff we have at our shop is 16ga. Which is only about 1/16" thick. But, I'll look around. I'll find something.
As for the screws, it's really hard to say. The entire bottom on the base plate has a type of foam on it. Basically to protect whatever surface you decide to set it on. I would imangine that the screws would go in from the bottom up. Notice the "L" shaped brackets and the location of the holes. I have a tap and die set at work too. So, I could probably place the holes where they should be and thread them to fit a screw. The end of the screws will most likely be concealed by the tapered plastic piece at the base.
I'll have to tinker with mine a little and see if I can figure out exactly how it is mounted. I'll let you know what I come up with. In the mean time, don't be afraid to play around with some ideas yourself. Just don't modify any part of the original stand, as doing so may compromise a perfect fit for the one I may try to make for you.
I'll keep you posted.
EDIT: maybe for a temporary solution, you could use some 3/8" plywood and mount it to that. At least it would stand upright and help prevent any damage from it constantly lying on its side.