I have a 22-250AI that my pet load for it is a Berger 80gr VLD at 3408fps, my drop chart says it is supersonic out to a mile.
The problem with 22cal bullets is spotting your shots at that distance, if you are shooting at a gong or targets at that range is one thing but shooting at rock chucks or other critters past 1000yards it is difficult to spot your missed shots. that is where shooting a 6,6.5,30cal or 338 is a much better choice. For example 2 months ago I was shooting at a pair of cougars at 1400yards, my spotter could not spot a single miss. if I would have been shooting my 338Lapua AI my chances of wacking them both would have been greatly increased
