Have changed the core a few times and learned more each time. Also have found different sized cores. 68 to 69 or 400 to 350. Not sure if it was the year or the size of the engine, but the housings seem to be all the same, you just need the right mounting clips and foam mounting pads. Also found that the thickness of the housing gaskets is important and will change the distance of the hose nipples from the block.
The core housing dose come out from the inside but the nuts to loosen it are on the outside of the firewall under the fender. You can save a lot of time, and having to remove the hood and fender (and risk scratching paint) by removing the inner fender to gain access. Not easy, but easier.