Agree, eFax is far from cheap, especially with the kind of bulk you are talking about, there are cheaper alternatives, it 'might' be worth going through the costings of it, 10 x Phone rental, Cost per Fax, then factor in the power consumption. I remember looking for an alternative to eFax and found a UK provider offering unlimited faxing for something like £30 a month? I didn't look into the T&C's, it could be that advertising business like the one described are prohibited from using such services :P
Anyway, good luck with your project, its certainly been an interesting read :)