The people to talk to are in your municipal office. Administration are the ones who deal with all that stuff. If you were to take your proposal to a Town Council meeting as a delegation and ask these questions there, I can pretty much guarantee that Council would differ to Administration for the answers, who in turn would likely tell Council that they will look into it and get back to them. After Administration provides Council with all the necessary details (budget, legality, liability, policy, bylaw), they would then take the matter to resolution and vote on whether or not to grant you the funds and or enact a new policy which would cover you under their insurance. Ultimately the decision is made by Council, if they decide they want to accommodate you, then they can likely make it happen.
The smartest thing to do would be to go to your Town office, and ask about your local bylaws and policies, Administration will be able to tell you what your best course of action would be. They could help you first of all by letting you know if it's at all a possibility, and if it is they'll help you write out a request for action which can be added to the agenda for the next regular meeting of Council.
You should have a member of Council who is assigned to your committee and attends your regular meetings. They're the ones that are supposed to be reporting back to Council and making requests such as this on behalf of your committee. Just last night we had a Councillor request an additional $10,000 for one of the Committees he's on, and they're gunna get it.
I actually just started a new job this year in government administration in a town in Alberta, everything we do in administration is dictated by the Municipal Government Act of the Province of Alberta (MGA), your local government is likely also regulated by such an act, so the process may be a bit different down there, but your town office is still the place to start.
A few recommendations for your committee: if you don't have one already you should try get a botanist on the committee, as well as someone who works for Parks, either with the Town, County or even the State. At the very least you should have a liaison who works for the State or National Parks. These people would be valuable assets.
I just talked to one of my co-workers who is on the Communities in Bloom committee here. She said for the most part what they do in regards to invasive species is education, they have representatives from weed control companies contracted by the Province do information sessions and distribute booklets on invasive plants to the community, she showed us the ones we have for distribution in the office (see Invasive Plants of the Crown of the Continent, and Alberta Invasive Plants Identification Guide). There's also the Alberta Invasive Species Council, who are undoubtedly an invaluable resource. If you haven't already you should contact the Massachusetts Invasive Plant Advisory Group.
As far as using commercial chemicals, only Town employees are permitted to spray here, residents are encouraged to use retail products to control weeds. But the biggest piece is education so residents can identify invasive plants, as many people can't distinguish between a pretty flower and a noxious weed.