Thank you all for your time and responses.  It seems pretty clear the correct cartridge length is 1.70".

JLewis has a good suggestion - cut a chamber using a 222 Remington reamer, and then cut the rim separately.  The challenge will be to get the headspace correct using that method - lots of small cuts and taking the barrel out to install in the receiver to check fit.

Still no reply from PTG on the cartridge length of their reamer.  Also, no reply from the reamer rental company on what they found out or what they will do to make it right.

JLouis,

Thanks JLouis.  Yes, I would use a cartridge to headspace.  I am a bit of a novice.  I have always hand-reamed the finish chamber cut to get a tight headspace.  I first check the short-chambered barrel for fit, to get an idea of how much material I am going to have to cut.  Then I put the barrel in a padded vice and give the reamer a few turns, then mount the barrel and check the progress.  For example, on a Martini Cadet I do this until the block rubs on the cartridge and barely will close.  A couple of more turns with the reamer and it closes without rubbing, and I am there.  I figured cutting the rim would require mounting the barrel in a lathe, centered and set to zero runout, and begin cutting.  The process of dis-mounting and re-calibrating the check the progress would seem make the rim-cutting process more time-consuming.  Is there a better way?

1isenough wrote on Jan 17^th, 2020 at 7:53pm:

From what I have read.
It is best to cut your threads and shoulder so it is one thou off the squared breach block.
Cig paper.
Chambered to fit that rim clearance as well.
All in one go.
You can just screw on the block can’t you without moving the blank?
It keeps tension off the pivots and block and undue stresses you don’t need on the cadet action.
Since you have no real leverage in seating or extracting a case.

Seating into the lands will help centre the case for fire forming.
The Case expands to what is what ,where it is of what you got.
From then on it’s just partial neck sizing and leaving things alone if you have too.
Unless you overly stretch the brass.

But then again I’ve only read about it.
And it sounded like good logic to me.
But I ain’t no gun plumber but I did cut a shit load of threads in a past life.

No and yes.
The clearance from the end of the barrel to the breachface being a thou.
The clearance on the few original cadets I have measured are from 5-8 thou.
The rim depth of cut has varied.

The end of the barrel face becomes the datum point for any extra free space you want to put into the system.
After you have established how much clearance you actually have in the barrel /breachface clearance.

At the end of the day your case will be well conformed to what ever chamber / free space you have provided for it minus contraction.

Tight chamber dimensions to a new case will provide less expansion and easier to get cases that are more uniformity consistent than a loosely goosey  one all being equal.

It don’t matter much after  you shoot a case a few times and don’t change it by squeezing it down in some form of die .

It will be fully perfectly formed in it’s expandable free space.

If the pressure of your load doesn’t compress all the compounded clearances and slop  in the system stretching your brass to much to make hard extraction of the case. 
Then we call that good don’t we???.

If you are rubbing your primers on chambering your pockets are too short for the primers you use.
Or you aren’t seating the anvil on the primer keeping them long.
One day you may experience lift off on closing.

If you are rubbing your primers on extraction you are either getting extrusion into the firing pin hole from excessive clearance there from mating surfaces.
The primers are too soft and or your load is too high.
It could be that you have just loose primer pockets.

I know nothing.