Update: I got the vise 'fixed'.
:-)

I say 'fixed' because after thinking about it a while (always good for me to do before diving in like a drunk diving into a frozen swimming pool).
I realized that the back corner makes no difference really, when the vise is clamping, the force is on the top of the slide, not the bottom edge.
Yes, the sides give the bending strength so the slide doesn't bend or break.
If I simply avoid putting big things in the vise and jumping up and down on the handle to tighten it, I can live with a less-than-like-new solution.

Here's a cruddy shot of it (the vise is mounted now and it's hard to see that back side of the slide)
Click image for larger version.  Name: vise slide fix.jpg  Views: 240  Size: 762.1 KB  ID: 37203
I attached a hunk of 3/4x1-1/4 to the slide with a 1/4-20 SHCS, and then welded the end cap on and put three more 1/4-20's through it into the slide.
It works!

Kinda (rather!) lazy-boy slummo solution, but it made me happy. (low bar there!)