Perhaps you could go the other way. Glue a tiny frame of wood around the reedhole in the reedblock and put the reed on top of it.
My wife uses a tiny electric drill for her jewellery making hobby. It has a lot of applications, including small grinders of different shapes that can me used to do shave of your reedblock. Almost like at the dentist :-)
Try moving the reed over to the opposing side so that the tongue has room to vibrate. If that makes the pull reed hit the other side then the chamber is too small and the blocks were not made right.