To be honest, I haven't been around for the initial lighting of a Blodgett pilot light.
Member waltertore has two Blodgett 1000s, but I think his safety valve is a little different than yours:http://www.pizzamaking.com/forum/index.php?action=profile;u=19066
Here's another member who hasn't been here much, with a 1060. They've got an email, though.http://www.pizzamaking.com/forum/index.php?action=profile;u=17126
One tricky part of this is that the safety valve on this oven was recalled back in 09, so other 1060 owners might not have your valve, depending on the age of their oven. Can you get a part # from it? That would tell us which valve version it is.
Here's an idea. If the safety valve button is stuck, you might be able to bypass it by heating the pilot thermocouple with a torch. Basically the button allows the pilot gas to flow so that it can be light with a match and then kept lit until the thermocouple gets hot enough and keeps the valve open. In theory, if the thermocouple gets hot enough, the valve will open. I don't know exactly how hot to heat the thermocouple, though. I do know that those thermocouples have overheating issues as well so be careful. I would take a torch, and, if you can, try 5" away for 30 seconds, then 4, then 3, then 2, then 1. You should also be able to take the safety valve out completely and test this with compressed air or possibly even a flashlight on at the end of the valve.
It's very rare that I say this, but I would post this question over at PMQ. It might take a while for a reply, but I know there are a bunch of Blodgett owners over there.
Since the safety valve is the first in the sequence, I would see if you can get the pilot light lit before replacing the thermostat. You might have to replace the safety valve AND thermostat, but let's cross that bridge when we get there.
Edit: Another thing to keep in mind is that even though you're not the original owner, if this oven has a faulty recalled safety valve, there's a possibility you might qualify for an upgrade. Did you get the original bill of sale?