Got around to doing the heater core last week.
The cowl does not need to be touched period. Just remove the in/out hose clamps to heater core from under the hood. Once the heater core cover is off, the heater core has one screw that needs to be removed. That screw is attached to a bracket clamp that holds the two heater core pipes apart. New cores come with the clamp.
The core itself is held tight by a metal retaining bracket that has two slots on top where the core slides in, and the bottom part of the bracket is a flat piece of steel that is springy. Once the top of the core is inserted into the bracket, pull down on the springy piece of steel to insert the bottom of the core. It's held in there good and tight.
I used the OSC 98485 heater core. This was a one piece unit. No installing the individual heater pipes. It came with a new bracket clamp for the heater core in/out pipes, and it also came with a roll of foam padding that was peel and stick. The foam goes around the heater core. Just look at how it's installed on the old heater core.