Million dollars question, I can ask a couple of people if they know his setup (maybe online you can find something).
A cigar cutter (Selmer SSS) would be on my gas list. Not sure he used one, but when I had one I felt like doing long glissandi.
Brilhart mouthpiece with a slightly harder reed? Maybe a good HR Link (4 or 5 facing) might work too. Selmer Soloist?
Johnny Hodges was famous for playing Buescher saxophones - Aristocrat models and then later on using the Le Blanc system saxophone for a while. Most photographs I have seen of Johnny he always seems to be playing the Buescher alto.
Mouthpieces? Probably a white Brilhart (like Charlie Parker) or maybe a Gregory. A larger chamber mouthpiece for a more rounder sound - I think Beechler might make a Brilhart hard rubber 1940s style mouthpiece.
Actually Coltrane (not Robbie) said Johnny 'Rabbit' Hodges was the greatest sax player on the planet.
Good luck but remember Johnny Hodges sounds like Johhny Hodges...