I was thinking 4BA but the screws won't go into a 4 BA tap more than a couple of turns. However, there doesn't seem to be a BSF that small. I reckon a couple of small 4BA screws will do the trick since the backplate is pretty thin and only has a small amount of thread in it. Should be able to get a couple of pan heads (or hex) on ebay (or similar internet auction sites!)
Just to confirm 4ba won't fit. What you need is a couple of 1/4" 6ba's. These work a treat. Just thought I'd post this up in case anyone has the same query in future.