Since you were watching for the center to be done and not going to a specific time, I'm going to take a guess that your oven is running 75 degrees of more high. It's not an uncommon failure. Confirm with a thermometer.
There is always some sort of adjustment associated with the oven temperature knob, when there is one. It may be on the back of the knob or under it, and it may make in one of a number of ways. Adjusting the zero position, adjusting the ring of temperature marks, etc.
BUT - unless it's obvious that something has slipped badly on the knob, like it just doesn't look right at all, it's likely the thermostat. The whole assembly will look something like this:
While it can be failure of just the thermocouple (the tubular device), it's easier to replace it, the thermostat, and the capillary tube all together. It's should not be an expensive repair ($50-$75 plus tech time), and I wouldn't advise doing it yourself unless you have some experience with similar jobs.
Of course, as already stated, check things with an oven thermometer to confirm the problem. If it's off, check for the minor adjustment around the knob, and if it's way off, have it fixed. It's almost certain to be the thermostat.
The clue to the likelihood of the oven running way over heat is the burning wax paper. Wax paper, when used to line pans (meaning all of it is under the batter, not exposed) will not threaten to burn until well over 350F or for a long time. Parchment might have done okay, because it can take more heat. But neither should be used to line cookie sheets and should not overhand pans where they are exposed to the hot oven environment directly.
And what you describe is similar to what happens when someone modifies a recipe so that it involves more or less batter in a different depth pan without properly adjusting both time and temperature. In this case, I think it happened backwards. Your oven changed the temperature, while you kept the same recipe.