Since I spent over a decade working in government and then 3+ years selling into all levels of government at my last SaaS company, I'll provide my initial thoughts here. But there are no easy answers to this question as the 15 days without a response can attest.
Your initial challenge (from the little I see about your solution) is that no RFPs will be coming out for your product since it isn't a common solution a large number of governments are already buying. At my last company, I had this same challenge and I overcame it to sell into over 20 states and 50 local governments in a few years.
Don't start with federal. They won't consider your solution until other governments are using it. I focused on state and local public safety. I did this by attending public safety industry conferences with booths and speaking slots. In other words, I built awareness.
Then I found the public safety employee that has the characteristics of an early adopter. Having customers that can produce case studies and be your telephone reference customer is huge.
I also setup partnerships with established companies that already have business in some of the large governments and states. It is so much easier for a government to find budget to add a service to an existing contract than bring in a completely new company.
Most importantly, I was able to work with states to established master purchasing agreement so local governments in that state didn't have to go out to bid. They could purchase off the state contract. It takes a lot of work for the first state, but when you have an example of one, you can replicate it in other states fairly easily.
I'm available for a call if you want to discuss this more.
