How to access the furnace - 2002 Cougar 279 EFS

I believe your 2002 is the same as my 2008.
If so, it would be a lot easier getting the furnace out if you cut a slot in the face of cabinet to allow the gas fitting thru.
You need to cut a little of the outside wood back in a slot about
3 inches long. The cut would be in your last picture right where the big red wire has that black connector on it. Cut the wood just deep enuff that the cover still will hide the notch out cut.
This makes the out and in of the unit almost easy.