Yeah, that is the ticket... To get seen in one place in order to get the gun to point in a particular direction, and then to sneak behind or to the side of it.
Strangely enough, after trying it perhaps 20 times last night and this morning, after I posted back and forth with you, I tried and it worked first time! ( )
Maybe it was because, some of the times I tried and failed, I took out my weapon from a crouch in order to have it at the ready... This time I didn't, and maybe that made a difference.
Ah, well... My little "crisis" is over. But if I get stuck again, I now know who to ask! But maybe this thread will be of use to someone else who gets stuck in a similar situation...