So seems what you are calling a false muzzle, is a guide bullet starter. Without pictures, hard to say when verbiage might not be correct to the part.
A guide bullet starter was most necessary for the picket bullet and without a rod with proper cupped end and enlarge part to fit the bore above the cup that fit the nose of the bullet
the bullet could not be rammed home and stay centered. That is vital to the accuracy. Of that bore size and rate of twist of 30", a short picket was about right.
The picket normally has an enlarged middle, with both ends tapered.
Guide bullet starters had a cup-nose that fit over the muzzle. A false muzzle, had 4 protruding pins that fit into corresponding holes around the muzzle. They only fit one way, so the rifling in the false muzzle aligned perfectly with the rifling in the bore.
It seems to me, the bore of the "starter" is a bit too small, asking for obturation of the projectile to match the bore.
To my way of thinking, it should be groove depth, but then, the actual muzzle would have to be crowned to allow the entry of the 'patched' picket - however, maybe Dphar can chime in here.
Closeup pictures are needed (imho), of the actual muzzle and the starter, please.