Mike,
As much as I love those old Stevens Favorite rifles AND the .22 Hornet cartridge, there is only ONE word for you?
"DON'T!!!"
The old Stevens Favorite action was made of "wrought iron", and never intended for anything other than the .22, .25, and .32 rimfire calibers it was chambered for. The barrel was very soft, low-tensile strength steel. It simply will not hold up to ANY firing from even a mild cartridge like the .22 Hornet.
The prop-up locking system will not resist the backthrust of any centerfire cartridge, nor even something warmish, such as the .22 WRM. Yes, I know, the modern-made Stevens Favorites are probably chambered in .22 WRM, but they are made of modern steel.
As a matter of fact, the scaled-up Stevens Number 44 and 44 1/2 rifles were finely made and finished, and many had a bad reputation for poor heat treatment and not holding up to extensive firing of mild BLACK POWDER centerfire cartridges of the late 19th century.
For your .22 Hornet project, please wait for and find a more suitable action. It's a really neat cartridge and shooter, but only in a properly made firearm.
HTH
John