I have heard the same thing with the vice, but don't trust myself to have the right touch to correct it. I have developed the sleeve it or don't use or fix it once and be done attitude in the last few years because sleeving will eliminate most of your AMAL wear issues and it's well worth getting rid of the frustration bad amals can bring. I have not had one of my sleeved carbs warp.
The tool consists of a flat piece of metal, a turned down bar that is approx. .004" smaller than the o.d. of a slide.. The bar has a hole in it through which a 3/8" fine bolt is passed through. The plate is threaded (actually with a Helicoil). All you have to do is shim the flange and tighten the bolt.
For an awful lot of bodies out there, straightening will all that is required. I have been using this tool for 20 years and it has become routine to fix new bodies that have been warped by customers over tightening the flange bolts or on carburetors customers want to save. And the beauty, it doesn't cost anything to do it.
Unlike a vice that can introduce more distortion, just in another place, this just reverses the original problem.
You do not want to take material off the slide or bore. The problem is the body is not round after mounting. First lap the flange flat using a circular motion with the body held by the flange. Back and forth will cause the flange to round in the direction you push. Make sure the mating face is also flat then mount the carb with no gasket/O-ring or anything else. Drop the slide in with a cable to pull it back out and no top on the carb. When it sticks, use a smooth jaw channel lock plier around the top to find the axis where the slide drops free. Take out the slide and gently squeeze the body in the same place then try again. Eventually you will give it just enough distortion to let the slide move freely. Only tighten the mounting nuts enough to squash the O-ring and nothing more. Only use Micarta (Bakelite) as the insulator, no gasket.
I thought the companies that provide sleeving checked the bodies for warping before boring and sleeving.
As I said above: The body will have to be straightened before it is bored. Yes, the people who sleeve these carburetors typically straighten them before boring. The wall is too thin to begin with, and removing any metal will make it more prone to bending when the flange is over tightened.
The warped bore goes hand-in-hand with a bent flange. If you have one, you have the other. Bend the flange back so it is flat and the bore returns to being round. Unlike at set of pliers, there is no guessing or skill required.
Most late Triumphs use an thick "O" ring instead of the phenolic spacer. It is important not to tighten the mounting nuts so the space between the carb. flange and manifold is less than 0.060". Any more guarantees you will bend the flange.