While I’m not familiar with your editing software (haven’t got the Vegas idea – where’s my rimshot?) Vegas is the video cousin of Sonic Foundry, and ought to have good EQ capabilities in its audio section. Boosting lows and getting rid of hiss are fairly basic operations.
I know someone who works for Sonic Foundry, so if you really get stuck maybe I can ask him a question or two, though I’d think EQ-ing a voice track is pretty basic stuff.
And frankly, your boss is being rather silly – there are boompoles alone that cost over $300. Renting for a one-time thing makes far, far more sense than buying something that isn’t even really designed to do what he’s asking you to do.