I work as an executive at a non-profit, and have worked in other non-profits. With that said, I don't think this makes sense as a non-profit. Primarily, you choose to be a non-profit if you want to get your revenues from donors. They are targeting government, and so unless they thought they could fund their program through governmental grants, it makes more sense as a for-profit where they are bidding on government work.
Keep in mind, a for-profit can have a social good mission and remain aligned to it (See Patagonia for instance).
Wouldn't the right answer to this be some sort of Public Benefit Corporation where the board does not have an ultimate obligation to maximize shareholder value? As I understand it, they're available in more than half of US states, including CA and DE.
Just because you are a for-profit does not mean you are beholden to pursuing profit at all costs. But yes, a B corp is another good option, though it has its pluses and minuses as well.
Keep in mind, a for-profit can have a social good mission and remain aligned to it (See Patagonia for instance).