Not sure I've seen the most recent materials. My impression is that for an AW, you need the specific permission by model, serial number, etc., from the head of the agency or a formally designated official of the agency. An AR pistol, I believe, is not on the roster of handguns in that it's not a "pistol" that isn't safe, so to speak, but it's by configuration an assault weapon (assault pistol?) due to length, magazine location, etc. There are handgun exemptions and assault "weapon" exemptions. So, I'd guess it would fall into the AW exemptions with related permissions, letters, etc. It would seem to me that you'd need to start with the agency to see what they will write up for you officially. Or a high powered firearms attorney. FWIW, I kind of doubt that the politicos were aware of AR pistols being something LEOS might need/want and were simply trying to keep the cops happy while messing with everybody else.
Remember, you are buying it for your agency. Maybe. Looks like I read they have to be surrendered to the agency but maybe the agencies can gift them on retirement.