However.....the 223 can be loaded down to 22 mag velocities AND use bullets with very similar BC's and designs as the 22 mag.
I have no idea on the powder charges needed (maybe around 10 grains), but there was a topic on here recently I think.
Try Sierra 45g Hornet or Hornady 35g V-Max for similar results as the 22 mag WITH a reduced 223 load. This is of course, if you are looking for less speed.
Also, a more comparable cartridge to the 22 mag would be a 22 Hornet or 218 Bee. These cartridges rival the 17HMR trajectory but do beat it by a margin. While the 22 mag still doesn't compare, they are much closer.