Hi Steve, I don't have anything to offer but advice, but I have made a similar request in the past, to companies that I had an on-going relationship with. Every one of them turned me down because of the "we would do the work" thing (and they knew I was very experienced at such things). That is a big risk for them to take, offering someone they don't know, time on their most expensive and important piece of equipment. There are many things that can go wrong (poor operation can literally destroy a hot press) and who is at fault if someone gets injured? Whose fault is it if all of your material turns to garbage and you think it is the press's fault? Many companies won't even consider using someone else's materials in their processes, because they don't know the quality or the specifics of that material (Will their adhesive work? Is the core flat and consistent thickness? What temperature and pressure do you need to run?)
I don't expect you will get a lot of offers. You would be better off sub-contracting that out and letting them supply the materials and labor. That's been my experience anyway.