Forget the little M1 Carbine. It is a different critter and actually the first assault rifle they just didn't know it at the time. It was made to replace a side arm for support troops.
Think Krag rifle and carbine, Or WWI Mauser rifles. There was the long infantry rifle and then a Calvary or Artillery carbine. Same chamber. Some had a different ammo that was less punishing than the main military ammo especially in the big bore carbines. When England went to the SMLE No. 1 they ended the two gun army bu adopting a rifle in the middle woth a 24" barrel. The US followed suit with the 1903 Springfield. Even now with the M16A2 and the M4 shoot the same round but have different barrel lengths. Heck the standard M16A2 is as short as an M1 carbine. But the M4 is more of a high tech sub machine gun. Maybe you want to look at an AR in the new 6.8 or an AR10 in .308, 260, .300WSM, or others. There is also the Spring field M1A scout or SOCOM 16. I just wish the Springfields came in other calibers like .338 Fed or .358 Win.
When I think of the Remington carbines I think of a woods or brush rifle that would give a fast swing and a powerful 30-06 /.308, round nose bullet to knock down deer or bear, but still have the accuracy and power to take a 100 -150 yard shot. The ultimate brush rifle.
I have one of the Deerfields you talked about and it is not a 150 yard gun. the .44 mag is not accurate that far with the peep sights set for 75 yards as a brush rifle. I thought it would be a great guide gun for our farm in NC and some of my fathers retired friends going hunting with me when I'm in town. I thought the big slug would anchor a badly hit deer in the woods and be short and out of the way if I were going to drive to their stand as well as dragging out their deer.
I end up carrying my Ruger M77 in .308 with Remington 180 grain soft point round nose bullets.
I think the short action bolt rifles have killed the carbine pump or semi auto.
If you are looking for a short powerful carbine look to a lever gun or see if you can get Ruger to bring back the No3 ( a Short carbine version of the No1) in calibers you would like to see as brush guns. I had one in .45-70 that I should not have sold. But one in 375 Win, 338 Fed, .308 Win,444 marlin or the .550 S&W would be great. Oh wait NEF makes the Handi rifle, a short single shot in the lighter or pistol calibers you are looking for at prices Reminton would not touch. One of the little Remington import mini Mauser's in 7.62X39 could fill the bill as well, but as a bolt action not a pump or semi. Sorry.