"Hardening (of gelatin) is slowed by acidic pH and is sped by alkaline pH."
Interesting...this is the opposite of what I would have imagined -- not doubting you, just surprised. In carbon printing we can put the developed carbon print in an alkaline bath to soften the gelatin and get it to release some of the pigment -- to lighten the print if over-exposed. Also the Part B of Kodak Rapid Fixer is the hardener -- and is very acidic, I believe.
Depends on the hardening agent: alums work differently than aldehydes. With aldehydes, there are apparently several different types of cross-linking, pH affecting the proportion and speed of formation. KodaK Hardener is alum based IIRC.