I can't speak to the professional considerations, as I'm a medical student. As a paramedic, I would rather have an EM physician any single day of the week. I've worked under a non-BC emergency physician and, with some exceptions, it was a nightmare from the paramedic's standpoint. It was basically like moving a mountain to get anything done.
I will say this: all of the best medical directors that I've worked with have an actual interest in EMS. Being in that position means being the bad guy sometimes. A medical director who goes out into the field, knows what they're talking about, and provides reasons for why certain requests are denied is someone who is going to have the respect of field providers. If you're going to speak on something that is not inherently medical (e.g. provide your opinion into an operational decision), make sure you know what you're talking about. Nothing irks paramedics more than someone talking about how something should be done in the field and being 180 degrees in a different universe. I've seen it a few times and it's like watching 30-40 people in a room instantly stop paying attention. EMS is a distinct profession for a reason, even if does have a lot of growing up to do.
Professionally, I don't think $125/hr for 5-10 hours a month buys a good medical director. Is this position more of a liaison between the hospital and the local EMS service(s) in addition to a local medical director or is this a traditional medical director position? Personally, when I was in a position to have a say in such things, I was always the guy at the local level trying to increase the medical director's contracted salary. To me $$$ = better talent pool when we contracted. As I left, I was starting to see some jurisdictions in our state actually write a preference for fellowship-trained EM docs, which I think was a positive.
Finally, if this is a medical director position, make sure you meet with management before taking the job. You can probably predict how things will be pretty quickly. Do they want someone who is involved or someone who is just going to rubber stamp stuff (red flag)?