Carb problem

[JCD]

I've an interesting problem, and I'm seeking advice from any carb gurus out there.
I just picked up a 1972 C10 with a two barrel rochester carb.
The truck runs really badly, and I suspected a vacuum leak, but never encountered anything like this before.
The carb base is still firmly bolted to the manifold, but the carb body is completely loose.
I mean LOOSE.
Three screws have completely backed out, and the fourth is so loose you can lift the carb up a quarter inch.
Is there any way I can remove the base without dropping one or more screws into the manifold?
I was thinking of sliding some sort of thin cardboard between the base and the manifold, but I wanted to hear some feedback from others that may have encountered this before.

Let me know what you think..
Thanks.

J.