I believe there is no advantage to controlled round feed rifles.
If you plan on shooting over 400 yards a custom might do you better than a factory rifle. But in most hunting situations, I believe, it is money wasted on custom, unless you just want something different. You do not need sub-minute of angle rifle/load combination for almost anything but long range.
I have some controlled round feed rifles. I don't hate them, but I would like to actually hear from someone who actually has had an issue with push feed rifles. In my opinion the issue is wives' tale.
I also have custom rifles. The one I like the most maybe be odd due to the above statements. It is a 375 Whelen AI on a Mauser action. (Good luck in finding ammo for that.)
If I were in your situation I'd look at Ruger's 375 Ruger (I know a controlled round feeding rifle). Or maybe a Remington 338 Win Mag - in bear country, I'd be feeding it heavy bullets and probably high grade bullets such as premium Nosler Partitions. A 35 Whelen or a 350 Rem Mag would work well too.
If you plan on shooting long range and want a "bear" rifle, I'd recommend a 300 WBY. You can get them reasonably priced in SS and a weather proof synthetic stock. I would further recommend something like 200 grain Nosler partitions. My factory 300 WBY rifles both shoot approximately .75 MOA with 200 grain partitions and they are both standard factory rifles.