Technical advice on this board never ceaases to amaze me! Of course the core comes out from under the dash. The problem is that there are 2 nuts on the heater box that are tucked in behind the fender. To remove them you have 2 choices: cut however big a hole in the skirt (that's not an option for me) or you can pull the fender.
The problem around here is that anyone who knows how to work on cars--rather than knowing how to talk about working on cars--is that the mouths have driven them away.