The pta system is pointless, but not for this reason.....mainly due to the fact that you've jumped through all the hoops to obtain your firearm licence... then need permission to buy an arm....
The act and regs (and enforcers) have confused calibre and chambering; the pta asks for calibre (=0.22 or 0.223 or 0.224inch or 5.56mm) but expects chambering (223Rem).
So calibre is the 'size of the hole' or size of the bullet, depending on what time of the day it is, so technically if you're re-chambering say 223Rem to 220Sw or 22-250, your not altering the calibre so no notification is required.....
But yes, if you rebarrel your223Rem to 338RCM.... an email to the registrar would cover you. Although, if you wanted to do some robin hood bow drawing; you could maybe argue that the standard manufacture referred to that model of firearm, as opposed to your actual firearm
Another avenue for say, a 338LM, but consider the reason on the original PTA must still apply, else you WILL receive a knock at the door at an inconvenient time.....