frame wrench

You almost always have to trim the barrel shoulder to get the barrel to align and with the correct amount of torque when fitting a new barrel.
When just correcting mis-alignment you usually don't need to trim the shoulder, AS LONG AS YOU'RE TIGHTENING.... NOT LOOSENING THE BARREL.
If you have to unscrew the barrel, you usually will have to totally refit the barrel by setting it back one full thread.
This is a BIG job and requires extensive tooling to fit the barrel and re-cut and gage the forcing cone.
While I don't really recommend it and it's sort of jack leg, if the barrel just needs to be unscrewed a little, you could use Loctite BLUE (removable) thread locker. DO NOT use Loctite Red (permanent).

While I have not done this, it's at least probable that you could buy a set of E&I frame wrench inserts and modify them to closely fit a Mark III frame.
You could do this with epoxy to "resurface" the inserts to fit, which while it won't adhere to the polymer inserts for long, it would probably do for a few times.

The wrench is not used on the barrel, it's used on the front of the frame.
For the barrel you use fitted barrel blocks.
Barrels with lugs are easy, plain round barrels can be difficult.
For the older round Colt barrels I used a miniature barrel vise similar to the hydrophilic jack barrel vises used by rifle gunsmiths.

To make a barrel block, get blocks of HARD wood like oak and rout a groove slightly larger then the barrel. Apply a release agent like a Johnson's Paste Wax to the barrel and don't wipe it off. Fill the groove with epoxy and lightly clamp it on the barrel.
let cure and remove. MARK THE BLOCK so you know which side it goes on and which way is toward the muzzle.
Then do another block for the other side of the barrel.
What you want is for the blocks to not quite meet when installed on the barrel. You should have at least a clear 3/16" gap between the blocks to leave compression room.

Thoroughly clean the wax off the barrel and blocks with paint thinner to leave them totally clean of oils or dirt.
Put the blocks on the barrel and clamp in a LARGE vice.
Again, if you have a barrel that has shrouds or ribs gripping them is no problem with a good set of blocks and a big vise.
Round barrels can be a problem depending on how tight they were torqued on.

For the frame wrench, you do much the same except you make castings of both sides of the fully disassembled frame.
You cast a frame wrench insert for each side of the very front of the frame.
The idea is the inserts in the wrench will completely surround the front of the frame and give full support to it.

D,

Thank you most kindly. You really answered my biggest question about NOT unthreading a little to get a run at tightening. My barrel is slightly undertightened. I have done a few Ruger round barrels, and yes it is easy to have them slip. Funny you mention marking the blocks as to side and direction. I have not checked my barrel yet, but I supect it has some taper ;^) I was afraid that putting any pressure on the shroud might be bad, but I guess like the frame, make as much contact as you can to spread the forces. And yes, I had thought about the I/E insert mods. I've gotten quite good with Accra Glass and Gel, and buy it by the big box. I use it like duct tape. A 1001 uses......

I still have to work out a final handload to confirm how much the barrel needs. And then a boatload of measuring on the gun to see it DTC is correct, and especially make sure I have cylinder clearance. Not in the mood to fiddle with the forcing cone. I swore after my last fixed sight Ruger I would never buy another fixed sight gun, but this one caught my eye. The nickel is perfect on it, and I really do not want to mar or flake it.

Thanks again,

Craig