Well I ultimately broke down and purchased a welder. It's a cheap little 110V unit but it's enough for whatever I need right now. After a couple weeks of practiced I figured I was ready and I started work on the new seat mount.
Here is the new seat mount tacked in place. The cross bars are 1/8" flat stock and the end pieces are made from 16 ga sheet. The "vertical" bar was originally going to be part of the mount (hence the seam weld) but I have since decided it isn't needed and its only purpose was to serve as a jig.
Once everything was fit into place I cut it out and made the anchor points. These are 2" sections of 1" x 1/4" flat stock welded to the back. I then drilled two holes in each and tapped them to M6 x 1.00. There are two holes because for whatever reason the holes in the bottoms of the seat brackets are at different widths depending on how you mount them.
I still have a little ways to go on the welding...
Finally, test fit on the seat.
The new mount is now fully welded into the car and I've removed the temporary brace but it got dark and the pictures started to suck. Testing fitting the seat in the car shows a total height reduction of about 1". I know it seems like nothing but at least my head is no longer touching the headliner with a helmet on. I figure I'll ream out the holes in the brackets a little to gain another 3/8" and I should be good. All that's left is to measure/cut/weld some 16 ga. sheet to box everything in.