I have a 2000 park avenue with almost 260k and the cat is completely clogged. Where I live we don't have any inspections for emissions or anything along those lines and actually work for a Ford dealer as a mechanic. I'm curious as to what the stock exhaust size is so I can go the route of cutting off the cat and replacing it with a straight pipe but want to get the right size along with getting the 02 emulators to avoid an O2 codes. Any help would be appreciated.

Just disconnect the down stream pipe, and shove a bar inside to breakup the cat. Start the car a few times and rev the snot out of it to blow it all out.
Next, go online and find an O2 simulator with your style connector.

I suggest you don't blow the guts of the cat into the muffler.

A quick Google search found an O2 emulator for $59.99 for your car, and a straight pipe is probably $20.00 .

Meanwhile, Amazon has a universal cat for this car for $49.46 .

If it were me I'd swap the cat out for a new one.

At the same time, I'd be really wondering why you are dumping so much fuel to clog the cat.

At 260,000 miles the cat probably gave up, maybe not clogged, but maybe a chunk came apart and turned sideways or something.