Greetings,
First, a disclaimer. I have never seen nor worked on a Progressive. I only know what I have read about them here and old Handloader magazines.
The straps are used to push the case into the shell plate thus aligning it with the dies in the tool head. A 38 Special case is 0.379" diameter and the 32 S&W Long is 0.337" diameter. So, with my trusty calculator, you need to push the 32 case 0.021" toward the center of the machine to align it with the dies in the tool head.
I measured a 38 shell plate and it gauged 3.614". My 32 plate measures 3.580". The internal bore is about 1.248" so the 32 plate "should" fit into the press.
The shell plates were machined such that when changing calibers you would rotate the shell plate 30 degrees out of index and adjust the straps so they just barely clear the outside diameter of the shell plate. This provides the proper alignment of the brass cases.
Since I do not care to modify the Star machines from original I have to reprimand myself for considering such an endeavor. If I had an original Progressive I would leave it alone in 38 Special. Perhaps one day I will stumble on to an original Progressive set up in 32 S&W Long.
Cheers,
Dave