To answer my own question, since no-one else has...

It appears that to correctly follow redirections, httrack needs the -u2
option. From the manual page,

Spider options:
-u     check document type if unknown (cgi,asp..) 
       (u0 don t check, * u1 check but /,  
        u2 check always) (--check-type[=N])

Using the -u2 option, httrack now correctly follows all my redirects.