I can easily get a 55 gr bullet to 4100 fps in my 26" barreled 243.
However, you'd be best off using a sabot if you wanted to shoot a bullet weighing 30 grains or so out of a 6mm bore, but it would need to be 17 cal, not 22 cal, in order for the sabot to have even material to properly support the smaller bullet. I don't know if 6mm/17 cal sabots are manufactured, but 30 cal/22 cal still are (as pictured):
I've shot 50 gr 22 cal sabotted bullets out of a 30-06, but it was at least 10 years ago. I put one shot through my chrony and it showed in excess of 4200 fps, but something dislodged one of the chrony's arms and that was the only shot I put through it. The bullets did not disintegrate - they all hit the target intact in a 4-6" group.