It can be a tough one, and I have been on the other side of things, especially since this state is so crazy. I was in process of my LTC when a Walther PPQ had popped up in state at a decent price. That was one of the best guns for me that I had fired and I was itching to get it. At that point, I had passed by background check, met with the police, been printed, all the paperwork filed, I was just waiting on the actual LTC and Pin from the state. I think you had done legitimate with your offer, and that was what I was hoping initially from the seller, let me put a deposit to hold, and actual purchase would be made after LTC had been finished being processed and exchange would be done at FFL.
Anquish buyers can set off alarms, which can be rightfully so, but it also depends on the conditions, especially when it comes to something that is rare and hard to find in the state and you are waiting on paperwork to complete. I don't think it can be a straw purchase if private, and if it is a gift from relative, that is fine. If it is a purchase through means of relative, that can be sketchy, but that also would be completely resolved if relative then sold the same gone and transferred after the other person got their FFL.
The moral of the story is two-fold here - Get legal and stay legal as soon as you can, so if you have the opportunity to legally acquire something, you can, instead of waiting and hoping on paperwork. Second, if you live in a state where you can't buy what you want because of tyrannical rules and AG, move out as soon as possible to some other state you can.