Who heads up the FD? It might be worth a face to face talk to explain the situation and how important you guys are. This stuff all to often gets political, which sucks.
Dealing with apathy or petty control issues? Then it is time to stir the pot. The head of the K-9 team needs to speak directly with the local council and make them aware of the situation and need for funding. Either arrange a one-on-one with the public safety liason, or attend a committee meeting - whatever it takes. Then once they have an ear, explain the current situation and mention that it was the original intention of the K-9 team to prevent costs to the community by obtaining available grant monies, however for some inexplicable reason the unit isn't receiving assistance from the FD in filing the necessary application(s). As such, 'free' dollars are being lost and significant costs are being borne locally. I'm pretty confident that silly hurdle you described will be addressed soon afterwards. Take it from someone who had been there, done that.
You seem to have a good knowlage about this subject and thank you for any info you can give. What do you do for a living? Just wondering.