From "Handloader's Manual Of Cartridge Conversions":

Make from: 9.3 x 72R.
Turn rim to .457 dia. and back chamfer.
Cut case to 1.55 and taper expand to .410 dia.
Trim to length and size in .401 die with the expander removed.
I.D. neck ream. Chamfer and full length size.
Fireform in chamber.

You can see why this book is not known for the most straight forward methods.

Ammo Encyclopedia tells us the maximum average breech pressure is 35.5 KPSI.
They also show that the original brass has a long tapered cut leading down
to the rim that may be necessary for the operation of the gun.
This will most likely not be reproduce-able from other brass.
Bullet diameter is .407"
Winchester dropped the cartridge (and gun) in 1936.
It was considered barely passable for deer.
The 405 was much more powerful (1200 F-P more)

My Cartridges Of The World (4th) has no conversion advice but does offer a couple of reloads:
24 gr. of 2400 under a 200 gr bullet. 2010 fps (max load)
31 gr. of 4227 same bullet 2100 fps (approx fact. ball)
28 gr. of 4227 under a 250 gr bullet. 1880 fps (max load)

(This is roughly the performance of a 44 magnum cartridge in a carbine).

This seems to be one of the very few cartridges that Ken Waters never shot or loaded for.

Good luck with your endeavor.
If it was me, I would shoot the original ammo, being careful to measure the velocity with a chronograph.
If the gun won't operate properly, the original ammo may have degraded some.
You might also consider having the gun stroked by an old-school gunsmith to be sure it will work safely.
The gun is a straight blow-back action, so you don't have to worry about gas pressure, but you do need
to keep the energy level within the bounds it was designed for.

---
Nemo