Closet Flange Replacement Issue

So, I've got the bathroom remodel coming to a close and I went to install the toilet flange. I have an issue with the Oatey Twist-N-Set (actually have the one with the three screws as well)PVC flange going into my cast iron pipe. It seems that when it is flat on the tile, I can't get a good seal. The gasket seems to sit halfway between the actual 4" pipe and the bell that the flange was sitting in so it doesnt seal well. I think if I cut the tile out a bit more and made the new flange sit flush, it might be enough to get the seal. If I do this, then I would need to use an spacer on top, right? Is that a good idea or would that be problematic?

Second thought was to call a plumber and have them lead in a new flange. Is there enough clearance for this to be done or would that have had to have been done before the floor was put back in? I guess I don't see how you could get lead to the joint?
Or is there something else that can be done?
I have included a few pics for reference.
Thanks for any advice!

I suggest it would be wise to have a new flange properly and professionally installed. Sure, ideally it should have been done before the floor was laid, but that's history now. All the more reason for a professional.