yeah, I would really doubt your core is bad.
that only stops water from one side. it is still a presurized system and would be spitting crap out if it were open.

It wasn't that bad to pull, but it was a lot of years ago.
3 nuts on the firewall you can see.
maybe a mount near the radio.

I have taken too many out, so I don't remember, but don't think there is a fresh air vent to unhook.
then just the cable to the valve on the box.

didn't even have to pull the front seat. It slid out under the dash.
Don't even remember unbolting that corner like you do for 66 and up.