besdor - It looks more like a early 50's or late 40s hat to me with the high untapered crown and unreeded sweatband. Brim may have been trimmed down to 2 1/4" so I don't know what the size the original brim was. I would guess 2 1/2" but I don't know. I'm not too familiar with the particular model.
The Alessandria model should also be a thin ribbon hat.
Borsalino got that liner logo trademark registered in January of 1976.
(the Purplesage hat)
Does anyone have a recommendation for conditioning the sweatband.