You could probably get a 30-30 barrel and have it rechambered. you would have to reload .308 bullets in it since the 7.62x54R is .311. You could have a smaller caliber barrel rebored to it but it won't be cheap. I've heard of people having a 30-30 barrel rechambered to 30-40 Krag. Go to graybeard outdoors in the forum section and look under the HR handirifle section and ask your question there. There are some on there that have some exotic stuff chambered in their Handi's like 376 Steyr.
You could do it with a 30-30 barrel as stated, you could even use surplus ammo if you had the gunsmith taper the throat longer like ruger used to do on the original mini 30's with the .308 bore, however the downside to that is reduced accuracy. If NEF makes one in 762x39 you could rechamber that as well, but would have to deal with a slower twist and not able to handle heavier bullets.