I would have no qualms about using an SMLE type rifle for hunting, just that it does not quite fit the American idea of what a sporting rifle is like, and probably most of us are indifferent to using them for such things. But it has had quite a long usage throughout The Empire with good success for such things as large game. A pure military rifle may not be the ideal configuration for hunting but if you wanted to sporterise one, I would choose one of the common No. 4 rifles for that task. There are plenty of cheap surplus No. 4 rifles in the US that are of no great collector interest and may need alot of help to be made into shooters, but if you find one with a very good bore and matching bolt, perhaps not too expensive. Aftermarket sporter stocks readily available. If you want to know how it works on North American game, maybe read up on how the Canadians use the cartridge and rifle. I think I have seen modified or replacement magazines that fit closer to the stock for hunting.
Your gun is like your nose, it is just wrong for someone else to pick it for you!