If you want to take forever at it, Corbin still sells dies for swaging fired .22lr casings into 224 bullet jackets and also sell a lead mold for casting the bullet cores. Far more practical, tho, is a .22lr conversion unit, from Ciener Firearms, for AK, mini-14, or AR-15.
i have done the exact samething, i use a lee 160 grain bullet .312 tumble lube. i do not put a gas check on it and load 9 grains of unique. the bullet goes 1350 fps. and the charge expands the case well to seal all the gases. my loads in a ruger gun scout are 6inches at 100 yards.
i use tumble lube, so you have to do it right so you do not lead the barrel, i mix alox with 25% paste wax and apply it twice to get a good coat. then flare the case like you do for handgun and you are set to load. last step i do is to crimp it with a really good crimp from a lee factory crimp die. (do not wipe the lube of the front of the bullet because it rides the bore and will lead if you wipe it off)
word of caution
MAKE SURE YOU DO NOT DOUBLE CHARGE WITH PISTOL POWDER!!!!!!!!!!
after i put powder in all the cases in the loading blocks i double check with a flashlight, the powder levels in each case.
i love shooting reduced loads, they accually are quite powerful with 650fpe and let me shoot my 308 a lot more and reduce loads are a great use for all the 308 surplus oddball cases i have. the noise is not that bad maybe a little more than a 17hmr.