I think you can/should remove the toilet flange completely, cut a hole in the cork to match the original hole in the sub floor. The cork should not add too much thickness to the depth of flange you'll need. You should be able to reuse the old flange. If you need a taller/deeper flange, you can get them at any large RV place. I used regular pipe thread sealant on the threads of the flange. Here
is a pic of Abby's closet flange.