If drive mapping don't work, your problem is most likely that System, the account TSM runs as by default, by default cannot access shares on the network. You need to allow NullSessionShares on the target share and host for that. Google will probably find you something useful; I couldn't offhand tell you exactly how to do it. You don't need a drive mapping BTW, I have tested with UNCs and that worked. Drive mappings are only defined in the context of the user that made them anyway, and it's inconvenient to set up drivemappings for the System account.
FWIW, I have a command file that calls blat on the server, which I start as a command admin schedule. GMail as a recipient works for me (it took setting up an Exchange contact for that). You could just schedule it, but I made it so that the mail would be sent from the same script that does our housekeeping.