I made a template to cut a piece of Aluminum tubing 1"ID and 1.25"OD into a sleeve for the ARK upper.
I have included the original ARK upper along with the one I modded to accept the sleeve.
I have not yet printed this nor have I cut the pipe, so revisions may come.

The upper only without barrel nut is 7in long, the barrel nut itself is 1in and the buffer tube is 6.88 in.
All in it is 15.3 in.
I am thinking a partial length buffer tube will give 12in with the tube extending from the barrel nut to halfway down the buffer tube.

As I said, very much a WIP.