Mine also has the brass screw. The thread pitch matches up with my 28tpi gauge very nicely. Diameter appears to be 5mm. 5mmx28tpi? Crazy, yes?
But I found
this French site which sells a 5mm x 28tpi tap.
But good luck finding a thumbscrew in this size!
The suggestion to tap it out to 6mm is perhaps your best bet. Looks like there is plenty of material to accommodate the larger hole.
Brent