Quoted from pencilneck:

A bit of an update to offer up... so while this took me some time because I'm going overkill on this, a standard replacement could be done in 1 day if you have the tools on hand.
0.5" MDF cut to size. This is my first time doing this and it boiled down hard core "measure twice, cut once", but with a lot more measuring and double checking myself over and over... and I got the length spot on the first try but the width was 0.25" too wide and I had to go back and cut a thin strip off the bottom plate. But with that, it dropped right in and was a good fit all the way around.
Once I was ready to glue in, I used Liquid Nails Heavy Duty adhesive. I cut the tip of the nozzle so I'd get just over a 0.25" bead and applied it along the vertical edge of the opening, just over the step/lip the base plate will rest on. A bead along the cross brace and a few gobs in the corners. Dropped the plate in and pressed down. I then went over the bottom with more adhesive, trying to work it into any gaps or openings between the cabinet and base plate. Then with a rag, ran my finger along the inside lip to help work the adhesive in and remove the excess adhesive.
Clamps, you really can't have too many on hand. Harbor Freight units here, so PBR beer budget going on.... clamped up and then let sit for 24 hours.
I went in with a chisel and cleaned up some of the squeeze out on the inside. I'll be making new corner wedge braces and gluing into place to finish up the job here.