Sorry, claddagh, .22 WRF is not the same as .22 Winchester Automatic.
Walt, if you could get one or a few rounds of .22 Auto at a bearable price, load one in the chamber and some LR in the magazine. Fire the Auto and see if the LR next up chambers. If it does, great, a barrel change would turn your 03 into a 63. If not, you will have saved a lot of work.
Frank DeHaas converted an 03 to take .22 WRM. It was a fantastically complicated project, including milling out the bottom of the reciever for a box magazine because he could not get the longer WRM to run through the buttstock tube.