You will get three shims from Fulton Armory, .005, .010 and .015. TYPICALLY, an M1A will need to be shimmed .015".
Take the trigger group out of the rifle and remove the stock from the receiver. Remove the handguard. Remove the flash suppressor set screw, remove the castle nut, remove the flash suppressor. Using a gas cylinder lock wrench and combo tool, remove the gas cylinder plug. Remove the gas piston. Remove the gas cylinder lock. Gently pull the gas cylinder off the rifle. Remove the front band.
Start with the .015" thick shim. Put it on the barrel until it stops against the barrel collar. Put the front band back on. Put the gas cylinder back on. Put the gas cylinder lock back on. As you turn the gas cylinder lock clockwise (putting it on) the gas cylinder lock should stop rotating freely at the 5 o'clock position as you face looking into the bore. If the gas cylinder lock goes past 5 o'clock you need a little more shim, try adding the .005" shim. If the gas cylinder lock stops at 2, 3, or 4 o'clock, remove the .015" shim and replace it with the .010" shim. Once you have the gas cylinder shimmed at where the gas cylinder lock stops at 5 o'clock, use the gas cylinder lock wrench to gently turn the gas cylinder lock to 6 o'clock wherein the gas piston and gas cylinder plug may be reinstalled. Reassemble the rest of your rifle then go test at the range.
Easy greasy!
OK, got it on your lap? Look carefully. If you screw the gas cylinder lock onto the barrel without the gas cylinder, you see that it "bottoms" on a little shoulder at the end of the threads provided for it. The real purpose of the gas cylinder lock is to locate the gas cylinder longitudinally, so that the gas piston has neither too little nor too much "combustion chamber" clearance with the bolt & op rod forward. Now, take the gas cylinder screw and hold it in the aperture in the gas cylinder lock provided for it. You can see that its purpose is to draw the gas cylinder forward, up against the gas cylinder lock, locating the gas cylinder in its proper position along the barrel.
The gas cylinder lock provides no primary "tightening" function. It is for locating only.
Is there any harm to tightening the gas cylinder lock with a wrench the extra half-revolution or so to get it aligned, instead of unscrewing it, so that the gas cylinder--and hence the front sight--is immobile?
You report that your gas cylinder can be rotated from side to side. This is caused by the splineways on the barrel being too lose with respect to the gas cylinder splines. Kuhnhausen's Shop Manual shows how to tighten these splineways by peening them gently, closing them up so that the gas cylinder fits tightly.
My first M1 had been match conditioned; it took a plastic mallet to remove the gas cylinder from the barrel. The gas cylinder lock had nothing to do with its tightness, as it of course had been removed at that point!
As to whether you doing any harm, I don't think you're doing any good as you're forcing parts together that weren't meant to be forced, at least not to that extent. You might even be distorting the barrel, a phenomenon noted with the flashhider on M14s. Here's what Clint has to say on the proper way to assemble and tighten your gas cylinder, gas cylinder lock, and gas cylinder lock screw:
Proper installation of gas cylinder and gas cylinder lock:
Tap the gas cylinder onto the barrel splines, then screw the gas cylinder lock clockwise onto the barrel until hand tight. Then, back it off until the the gas cylinder lock plug hole is at the 6:00 position, enabling the installation of the gas cylinder lock screw (gas cylinder plug). Tighten the plug firmly.
AND,
Be certain that the gas port hole of the barrel is more or less centered in the gas cylinder's gas port window, which is clearly visible when looking into the mouth of the gas cylinder.
Tightening of loose/wobbly gas cylinder:
Remove gas cylinder plug, gas cylinder lock & gas cylinder. Then with small ball peen or cross pane hammer, or, with a 1/4-3/8 pin punch or a 1/4-3/8 ball bearing and a small hammer, firmly but gently peen the 2 walls of each of the 3 splines. This will gently "crush" the walls thereby narrowing the spline-way. For a match rifle, add a small bead of red Locktite 271 in each spline-way. Then, tap the gas cylinder in place (it should require some tapping force), and follow the installation instructions above. Be sure to clean any excess Locktite before it sets.
Important Note:
If the barrel in question is a collectible, do not peen it. Leave it be, or, use locktite to tighten the cylinder in place.