AFAIK, you only have two choices. You can change one of the handlers to run at a different request stage, or you can replace mod_usertrack with Apache::Usertrack and used stacked handlers. Stacked handlers are only available for Perl handlers, so you can't do that with the original mod_usertrack.
There may be some compiling trick to adjust which one runs first. Asking on the mod_perl list is your best bet for that.