Newtosavage, I understand where you are coming from, it seems like "you" are an unethical hunter for using a smaller rifle than what is popular today. If you look at the hunting loads for the 30-06 back in the day (that were used for hunting all of North America's game, including brown bears, you would see a majority of the loads can now be beat with a .308 on energies. It's silly to say that we need more nowadays, when we have had dramatic improvements on bullet & powder technologies, that have squeezed quite a bit more efficiency out of previous cartridges.
Now in saying this I understand that having a caliber that is overkill for game isn't necessarily a bad thing, but to out right call people unethical for hunting with a lesser cartridge, without first hand knowledge of the shooters abilities is ridiculous. A more important question is how good of a shooter are you? And are you willing to pass up a bad shot, or force it? And are you willing to stalk the game to get a better shot? If the shooter is a 2 MOA shooter or less at 300 yards, that will place the bullet into a 6" circle which with the right bullet, will kill a deer ethically a majority of the time with many cartridges.
Back to your question it seems there some good cartridges out there that could meet your needs. If I were you I would take a look at some of these:
Faster velocity, flatter shooting, smaller bullet
.243 Win
.257 Roberts
25-06
Medium-Fast velocity, flatter shooting, medium bullet
6.8 SPC
6.5 Grendel
Fast velocity, flat shooting, medium bullet
7mm-08
6.5 CM
260 Rem
280 Rem
Slower velocity, larger bullet
30-30 Win
.300 AAC/Whisper
7.62x39 with .308 bullets
If you are truly wanting something that's in between those cartridges the one that fits the bill is the 30-30 Win, with new technology and in a bolt action where you have the widest range of bullets would be the ticket for your desires. But if you don't care about sticking with the .308 cal, then the 6.5 Grendel, 6.8 SPC, 7mm-08, 6.5 CM, 260 Rem, and 280 Rem might be of interest.
I wouldn't look past the 30-30 Win however, most of the information and preconceptions about it's abilities, velocities, flight path, etc. are based off older bullet technology. And with shooting a bolt action with modern bullets and powders its a pretty sweet cartridge.