I haven't tried it but can you upgrade those browsers without administrative rights? I am assuming you can't do it on corporate settings.
- You could do it as Chrome does and have a per-user install. I don't think Mozilla wants to do this.
- You could install a service or a scheduled task to do the work for you.
- MSI updates can be installed without admin rights if they're Authenticode signed, and Mozilla does have a valid Authenticode digital certificate.