My brother had a Pederosoli Kodiak 45/70 and it regulated extreemly well with several divverent loads from factory 300 grain to my souped up 405 grain loads. It shot Cor-Bon and Garretts Hammerheads into the same group at 50 yards as well.
Levallois, Try and find a Kodiak and test fire it.
Or maybe you could find a used Chapuis in 9,3x74R fairly close to your price limit. I am very happy with my Chapuis 9,3. I have hunted with it quite a bit here in the States as well as a black bear in Canada and plains game in ZIM.
My 9,3 is scoped and that really adds to the versatility.
It is my favorite rifle under .40 cal.