Well I ordered the laminate from Home Depot. Its pretty thin 0.039" and comes all rolled up in a box. As you can see below it is a bit more red than the panel it will replace but I'm going to go with it.
The next step will be to get a thin backing board so that it is the same thickness--or a little thinner than the current panel and use some contact adhesive to glue it on (there will also be screws going through it holding the counter).