All great advice, but I must point out one obvious omission. You can always get a little aggressive with it if all else fails.
You want to get your "swing" locked in and lined up, Before your trailer touches the trailers sometimes( if yheres 4 inches of clearance). The desired goal is to accomplish this and whip the truck around ( where you can see both sides) about 6 feet before hitting the trailers. If you're very cramped on swing around room, it helps to have tandems all the way back. Sometimes it's the only way .You can fight that tail swing, keep jumping out, or quickly slide them. Definitely try to stay under the trailer, not total L shape at the last second. It's possible to rest on the trailer and can't pull back out without scraping it. It's all about angles. You just have to practice and you'll be like those yard bosses. They have an advantage of a reall short wheelbase for crazy maneuvers, that you just don't have in a sleeper cab. Jmo
If its gonna be that tight, I always say "#### it", and find another place to back in that leaves at least 2' on drivers side, and a foot or more on the off side. I ain't doing the limbo under a trailer to get it off my tractor.
I don't like holding people up. Trust me, I looked for a double spot. That DC was very crowded. Goal 1,2,3 Thanks. I was thinking something like that, but I was close to the trailers already on the other side. I have done the L shape mistake a few times when I was bran new. I would get it lined up, but I would be shaped like an L. "Well, what do I do know?" LOL Fortunately I'm past that. It's like I was just off by a little bit. And I was afraid to get closer to trailer on my sight side because I was worried about that resting position you spoke of. I've seen something close to that happen. Somehow you get it lined up just right and you can't pull it out. Or at least it's very hard and takes a while.
In a really, really tight spot, if possible get lined up, back in just till the landing gear is at the front of the trailer next to you, crank the landing down til an inch or in the air, pull the fifth wheel, then back the rest of the way in. Then drop the air bags, unhook air and power cable, pull out from under trailer.
I've several times left the trailer sticking out so I could get to the dolly crank without climbing under a trailer. Once dropped I'd flag down a jockey and have him push it back. I've also done the reverse. Got a jocky to pull a trailer out so I can get to the crank.
If I have the room and the spot is tight like that I like to use the 45 instead of the 90. That tail swing isn't as bad at the shallower angle.
I’ve had yard dogs pull out a trailer from a tight spot, at least far enough to crank up the gear. I reckon there’s no shame in asking them to back it in if it’s that tight.