What happens to the bullet as it transitions from supersonic through transonic to and then into subsonic flight depends on the bullet design. A rounded nose bullet that is short for it's weight will do just fine but it's performance in supersonic flight will be dissapointing because the BC won't be very good. A bullet with a long secant ogive and real high BC, (SMK and VLD for example), will not do as well in transonic and subsonic flight, but they will go a lot farther before they get into that speed range because of their high BC.
My buddy has a .300 Whisper. He was having trouble with bullet stability shooting the heaviest SMK he could find - it was going sideways through the target at 100 yards. His timing was good - I'd just finished reading the chapter on stability in Litz's excellent book. Based on what I read in the book I suggested he go to the heaviest round nose bullet he could find. He did. It made nice round holes at 100 yards. Problem solved.
A .308 is used a lot on paper at 1,000 yards - I don't see that cartridge as a 1,000 yard hunting round although it might work for coyotes.
You mention a 7mmMAG. I havent' hunted with one ... yet. I just got one. Studying the ballistics for that cartridge has been interesting. It looks to me like it's a viable 1,000 yard cartridge for whitetail and smaller game with the right bullet. 7mm bullets have higher BC for their weight than .308 bullets. 7mm seems to a caliber where it "comes together" for long range shooting of high BC bullets out of a viable walk around hunting rifle with out a muzzle brake
(a feature). Another one seems to be .338 but almost always with a muzzle brake unless the rifle weighs 20 lbs or more.