Try calling around to different NH PD's and ask them how to donate to local fallen officer/firefighter causes and the like. We have local public safety causes and charities where I work. If an officer, firefighter, or ems are killed in the line of duty, the family of that person receives help directly from these local causes. For example, here is one of our local public safety causes.
http://www.200clubwakecounty.org/
The calls you mentioned are just what you said. They soak up too much of the donation money to make the donation worth it and who knows where what is left after that goes. Giving and supporting locally goes a lot further.
You do not even have to give anything. Stopping by a station to give a kind word is priceless. I like when I get those!