I've been able to shoot with the 3x on the patrol. But my 3x was modified in two ways. A locking screw was adding to the pressure clip. When the magnifier is installed on the focus ring, this locking screw is tightened to exert enough pressure to prevent movement. That part works fine.
Secondly a hole was drilled in the threads that connect the magnifier to the locking ring. A set screw was added. Normally this set screw "hides" down in the threads of the magnifier. But when installed on to the locking ring, the setscrew can be backed up into the hole in the threads on the locking ring thus preventing the magnifier from moving in the threads. I've shot that off .22LR and 556.
With the .22LR never had an issue. With the 556 with enough rounds, the screw will unscrew and then the magnifier will move in the threads. That throws off your zero. This can be prevented with the mild loctite. But of course then the magnifier has to be removed from the patrol with the pressure clamp instead of unscrewing it. Removing and reinstalling with the pressure clamp would not be a zero retention process. So for shooting off 556, the magnifier needs to be installed on the patrol in such a way that it cannot be removed without disturbing zero. Its sort of like you converted the patrol to a reap-ish, but the process is semi-permanent. And to remove the magnifier is also semi-permanent. You can't just attach and reattach the magnifier in the field for shooting without disturbing zero. That's the bottom line.
I have not tried shooting with 308. I suspect it would work fine using the same process used for 556 (loctite).
But, as you can see, shooting with the magnifier is not an "out of the box and it works" sort of activity. Its more like a "you can make it work if you pound on it" sort of situation.
Or for a shorter answer, go with Choid's "You don't want to shoot with a magnifier"
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Also, in general, you need a clipon to be 1x magnification period. That's so your reticle will be usable. If the clipon is not 1x then your reticle will be compressed (or stretched) ... and a mil on the reticle of the day scope might be 3 mils on the backdrop of what is seen through the scope.
Now you can use the center of the cross hairs regardless. Or you can dial the elevation/windage. Its basically like an SFP.
The skeet was designed to be a clipon for an ACOG ... the skeet being 1x and the acog being 4x. In that use case, it works. If you want a long distance thermal clipon, they make those also. They're call UTC-xii
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I did try an experiment with adding the USGI 3x (PVS-14) magnifier to the rear end of the patrol (the threads don't match exactly, but they were close enuff that I could get the 3x to lock on well enuff not to move when being fired).
I'm sure the reticle isn't perfect (re-stated I'm sure the rear end demagnification doesn't "exactly" match the front end magnification ... i.e. one 3x is not the same as the other 3x ... but it was pretty close.
But all this is essentially trying to build your own thermal clipon. You can do that, or you can buy one somebody else already built. I've chosen to go that route. I now have two UTC/x thermal clipons they both work great ... and I have a skeet and patrol and breach and a coti for head mounted thermals (and 3 PVS14s and 2 PVS9 NV clipons) ... so I'm using clipons as clipons and spotters as spotters ... and I'm happy doing it !!!