I don't want to come across in the wrong way, and I'll admit I have a hard time concentrating when a beautiful woman is talking. I'd probably be in the "let's not pretend I can concentrate on her words" category.
The attention you're getting is sort of "high intensity, low quality" attention. You can abuse it to generate the desired sort of attention. Think of them hitting on you as an indicator of their interest, and just talk through it. If they're to brazen, correct them. Basically remember you're in charge of the conversation.
Don't be mean about it, at worst ask them if they need help concentrating on the issue at hand. This attitude of "you're distracted, I'm not romantically interested, but enthusiastic about building a connection with you" is probably delicate to establish. There will be a lot of men initially confused: many have never seen an intelligent and capable woman carry herself before. Pat yourself on the back over doing true feminism.
Also - try to remember it's hard for everyone. You can never be certain it's because you're female.
WRT credibility - welcome to "alternative medicine". Try to keep the alt-med vibes away, because people have their allergies around it, and consider everything touching it insanely stupid. The placebo is powerful enough that it could make you feel better. Perhaps present research.
Throughout writing this I'm wondering "how eye catching is very eye catching? How would she look?". I guess that validates my first paragraph. If you're dealing with someone like me; understand that virility is a pride and a weakness. We can't help it, we hate ourselves for it, but it does make us strong and virile men, and there's a sense of pride to that.
Honestly the best reason for separating women from business is because I just can't handle the distraction. I imagine a lot of men are more like me than they'd care to admit.