Nice pair there. I'm sure that you are going have a blast with the new heater.
The problem with the mags is that the receiver on the SA version was reduced in height by .1 inch. This was done to make it much more difficult to convert an SA version to FA using FA fire control parts.
This had the side effect of displacing the mag catch in relationship to the cutout in the mag. There are two choices for those who want to use mags made for the FA Thompson.
The most common choice is to alter the mag by enlarging the cut out in the mag by .1 inch. This ruins the mag for use in an FA Thompson.
The other way is to alter the mag catch. This is done by removing .1 inch from the top of the mag catch. When doing this, you need to maintain the contours of the catch. Here is a link that shows before and after photos.http://www.machinegunboards.com/forums/index.php?showtopic=14128
The two biggest advantages for the second option are that you only need to do it once and that you are not ruining the mags for the full auto Thompsons. After all, they are not making any more.
Another advantage is that should you end up with an FA Thompson, you will be able to use the same set of mags for either firearm.