I am unsure on all the laws in different states. I do know based on the actual weapons we are talking about here some Nazi states will not even allow a commissioned police officer own or purchase these even if it is for official use.
But as far as BG checks, normally how it works outside the state I live in would be you find a FFL holding firearms dealer that is easy for you to use, they will fax me a signed copy of their FFL and I ship the weapon UPS per instructions given by you guys and you go pick it up. The gun shop you choose will have to do what ever is needed per state to allow you to pick it up and take ownership. In my area the local shops charge a fee, generally $25-$50 bucks which is normally what they have on firearms as a profit margin. It is stupid in my opinion but they do it all the same.
If you are an LEO sometimes they will wave those fees. Like for instance, new glocks should cost civilian customers around $450-$475. This would be a standard glock with no night sights and 2 high cap mags. What Glock does for LEO is add night signts and a 3rd hi-cap mag for close to the same price and if you use department letter head no taxes.
So all in all it is a better deal but still nothing to get excited about. The cost for new glocks in bulk is pretty cheap.

