"do you think it'll fit the old square-back Brownings"
watch this video,
http://www.youtube.com/watch?v=B__2cFEp89M
semi-autos mount a little differently, they don't use the 'breach-post', they use the trigger blocks. The rounded rectangle hole in the top is where your "charging handle" thingy sticks out.
I can't answer exactly, but do this as a close estimate.
draw a rectangle 7" x 3.75" - this is the inner-dimensions of the main 'box'
draw the rounded rectangle hole, which is 7/8" x 1-7/8"
this hole sits 1/2" from the top and 1-1/8 from the right
if your gun is higher than 3.75", then it won't work
if your trigger guard sits outside of the main box, then I don't think it will work.
if your charging handle doesn't fit through the hole, then I don't think it will work. (this gets tricky though, should handle be in rearward position while storing?? Idk)
In a perfect world, you would have an inch or two of room where the back of the trigger guard isn't too close to edge of the main box, this way the trigger block could do its job. you could easily alter this thing and customize your own trigger blocks
in the video, the gun is facing left, yours would face right.