I found in the past that it’s easy to get part (just a few thou) of the thermostat flange sandwiched between the non recessed part of the housing and manifold
I take a string and a small dowel. Loop the string around the top of the thermostat, out the housing opening and around the dowel. This hold the t stat in place while I put it all together. I agree see if it can move after is good insurance
