Shelly,
First, color me jealous of that rig. Just. So. Much. Awesome.
Second, about the worst that would probably happen is some mild discoloration of the underside of the shelf. But that would probably take a lot of time. When I had a similar lack of space at work the underside of my shelf got slightly browned, but no worse and that was with 8-10hrs of continuous runtime. The 6SN7 is also not pumping out that much heat. If the data sheet I found is correct it's probably only trying to deal with ~4W (6.3V/.6A heater) but don't hold me to that. My DIY skills are eroding with time and it's been a while since I applied much, if any critical thinking to stuff like this.