Here are the pics as promised:
I filled in the holes and lightly sanded the surface of the mdf.
Here's what I used to apply the veneer: TitebondII and a foam roller.
Here's the veneer drying. I first wet down the wood side of the veneer with a damp cloth, then rolled the glue on with a roller (the water helps the veneer lay flat... without the water applied to the wood side, it would curl when the glue is rolled on). I put on two coats in rapid succession and set it aside to dry.
I rolled the same two coats of glue on the mdf substrate. I let everything dry for about 45 minutes.
After both sides were dry, I put the veneer in place and taped it at the corners (only to hold the veneer until it was ironed down in the center).
I put an old cotton t-shirt on top of the veneer prior to ironing (to prevent the iron from scorching the veneer). I let the iron heat up to it's highest setting (cotton/linen), low steam, and began working at the center of the veneer. I moved slowly from the center outwards, keeping steady pressure on the iron. Once the center of the veneer was done, I removed the tape at the corners. Then I continued to work from the center to all edges.
I removed the t-shirt and checked the surface for any bubbles or other places where the veneer had not adhered... especially the edges (I didn't find any problems). Then I put the t-shirt back and repeated the ironing process one final time (again, working from the center to the edges).
I had cut the opening in the veneer (for the plate amp) so that it was about 1/4 inch smaller than the opening in the mdf. Once the veneer was cool, I worked with a veneer trimmer and 220 grit sandpaper to trim the veneer back to the opening in the mdf.
Now, it's ready to have the side/leg and trim pieces attached, then the top.