Scooter B:
I have always thought the "there's nothing we can do" thing is one of the weakest exscuses in the so called "professional" sound industry worldwide. As far as I'm concerned the engineers that have told you this should have both the equipment and capability to do what you want, after all they are working for you not the other way round. Depending on the size of the gig you may not even need to mic up or DI but when you do need that extra bit of ooomf in the mix your engineer should be able to mic you up. It is NOT a difficult thing to do and the noise thing (I'm assuming they mean feedback) should not be an issue if they can tune a system properly. Even if they mean noise as in hiss it still shouldn't be an issue, how many times have you noticed "hiss" when you've got 5,000 watts of rock music blaring at you? But all that said, at the end of the day in a live situation a DI is the quickest and easiest but not necessarily the best for the individual.
Mic wise, the rule of thumb is that if you can use it on a kick drum you can use it on a bass amp! AKG D112's or as I mentioned earlier the Peavey PVM520i are both good mics that I use regularly live and in the studio.