The Stevens 44-1/2 action was not designed to operate at pressures produced by most of the cartridges suggested. A more realistic list to choose from would be:

22 Hornet
22 K-Hornet
225 Winchester
25 Hornet
25-20 Single Shot
25-35 Winchester
30 WCF (30-30)
30-40 Krag
32-20
32-40 Winchester
8.15X46R
348 Winchester
38-55
45-70
45-90
45-100
45-110
7-30 Waters

Of these, my choice would be the .25-35. It's about the diameter you specify. Factory ammunition and cases are available. It will meet your requirement of 2500+ fps with medium weight (for caliber) hunting bullets if hand loaded. If you needed a little more then why not chamber it for .25-35 Improved? You could still fire .25-35 factory ammo in the rifle. The .25-35 is one of the most "Improved" cartridges and benefits by a velocity increase of about 25%.

~