No doubt, your approach HAS to be stealthy. Everything has to be dead on quite. At that point, your casting has also got to be stealthy with an ultra light presentation and light weight flies. Your target is never the fish. It's always 3-4ft off the water and allowing it to fully unroll out and then drop your rod, allowing it to settle on the water, NOT crashing on the water. And please, try to cast without rocking the boat, because laid up fish will feel the boat rocking more than any place else. That's where I'm casting overhead for accuracy and to help keep from rocking the boat (with my stance straight facing the fish and not a side stance). The stick of choice will be a 10wt for that situation.
Ok then, let's break it down, step by step, moment by moment, situation by situation.
If they are all pointing in the same direction, that means they are all facing into the current. You need to determine how much current there is before you make your cast. If the current is moving pretty quickly and they e holding t same location, then they are expecting food to come their way and therefore will spook less and make quicker decisions weather to eat it or not. This is where you can get away with a slightly larger fly. But they are also expecting the bait to be spooked by the fish when they see a predator like a big poon and so are expecting the bait to dodge them when it gets right up on them. So your approach can be almost perpendicular to the fish and better yet, more down current from them, throwing up at a 45 degree angle up and past them. The trick is getting your timing just right so you throw uptide about 5-8ft in front of the lead fish and about 3-4ft past it and have enough time to straighten out your line, leader and fly as you strip it into position at least several feet directly in front of the fish as the current bring it to them, all while you are getting all the slack out of the line with the rod tip touching the water. I like doing this off the casting platform because at this point, they can spot you just as easily as you can spot them. Wait, what do I mean by that?? I mean, you could have already shut them down just because they saw you, even tho they didn't spook.
When the fish are in this pattern, think of dry fly fishing to spooky brown trout, except more than likely, you'll need to be bumping your fly and all the while keeping the slack out of it.. So again, the idea is to get the fly in front of the fish about 2-3ft out in front of it, up-current from the fish and then bumping it towards you, taking it away from him to one side. At this point, the fly will be about a 1-1.5ft from it's nose and out to the side at a 45 degree angle from it's near side eye towards you. That will be the decision moment for the fish. It's like swinging a minnow pattern at that brown trout in the river, holding on the other bank and allowing it to swing past it's head to get it to commit. So, as soon as you see its head turn, make your bumps longer, where you are slightly picking up the pace and if he's keyed in on it, it will fully commit when it get's to the side of it's head.
Here's where it get's a little tricky. With a bunch of fish sitting there in the current, they all will not be in-line with the other in a laid up situation. So they will spread out some. So the next fish behind that one might pick up the sight of the fly and you continue your bumping and then you are then trying to get that fly in front of the next fish, which will lag behind the lead fish and to it's side. In that situation, I've had the lead fish refuse it and either the 2nd or the 3rd fish get aggressive and eat it as it past by them.
Like backbone mentioned, you are also trying to get that fly at eyeball level, or a little above that, during your drift approach to the fish.
If you drop it on their head, you can blow up all the fish and it's over. I would never recommend that. That's how you catch pacu in the jungle and LA redfish, not spooky laid up poons.
If the current is slower, then you can tighten up things and get it a little closer to them. But this is where you need to down scale the size and weight of your fly some. If there is virtually no current and they are still holding in that pattern, you could get more uptide from them and throw down to them and past them and then bring the fly up past them so they can see the fly from there far side eyeball and see the fly moving up and away from them and a steady bumping pattern. Then they will kick forward to come and follow it, but in that case, don't speed it up.
If no current and they are just randomly facing in different directions, Then they are not necessarily feeding. In either "no current" situation, you should further scale down the size of your fly, but the fly still pushing some water like a small mullet or minnow pattern. So no current means no food. If they are not swimming dive-bombing prey, then again, no real food coming their way, unless the flat is just covered up with a variety of bait. So they may just be hanging for a rest and waiting for the tides to start moving. Yet, like we say, there still always room for a potato chip!
So in this case (no tide/current situation), try to find one that you can throw on (an just not the biggest fish either) that is facing in a position that you can get off a 45 degree angle shot from the fish where you can then cast past the fish and pull it by it, where it is seen by the fish at eyeball level (or slightly above) out about 1-2ft or so, but the pattern of the fly is somewhat swimming away from the fish towards you. So you are getting the fish to kick it's tail and follow it with little effort without you lining another fish and without causing your fish to spin to the side to try to eat it. In other words, they want to eat without committing to too much work, but without being spooked, cause they always need a moment to look it over before they'll eat it.
IF they are facing away from you with no current and you cast past them and then pull it directly back towards them, it will spook, because it's un-natural for a bait fish to swim right at a predator when there is no current, and these fish know it (or maybe it's like the mouse that runs towards an elephant
or something like that).
If for some reason, you find them chaining, tho prematurely and still in the Keys, well then that's another subject. Sometimes they will do that on a wider open flat in more of a pre-spawn hype, getting ready to migrate somewhere to spawn. That is where they will let their guard down a bit. But you said all males? Yes I know! Maybe it's the bigger guys teaching the little guys what to do when the time comes. IDK! Lol
Anyway, if it happens, just be sure to throw past the spinning circle off to the side, on the side that spins back towards you, like you are throwing a tangent to a circle and taking it away from them, but bringing it close enough by them, so the fly is spotted.
Anyway try that the next time and see if it makes the difference.