I wouldnt be too sure on that one, a centrefire for fox is a centrefire for fox in most licensing depts eyes.
If it were a .243 or a .222, if you havnt used a centrefire before then they may still insist on mentoring.
However, seen as youve shot a rimfire for a good few years with no problems then they could let you have one without supervision, the best thing to do is ring your dept and see what they say, most are quite helpful it seems, they are there to give advice on these matters, and if they say you have to shoot with a mentor then just, go and Zero it with your mentor and have a few c