A/C blowing warm, again

A leak that large should have shown up when they tested the system. Out of the items you listed the evap and condenser cores, lines, compressor, dryer, service ports and switch all could be leaking, however with a leak that large I would look for an area that is now dark and oily as the refrigerant leaking out would have carried the oil with it and that should leave staining and a damp area. The first thing to do would be to put a set of gauges on it and check the pressures in the system, it's possible it's a leak, but it could also be a faulty switch not allowing the compressor to engage.

https://www.2carpros.com/articles/re-charge-an-air-conditioner-system

shows some of the process to test the system. You can usually get the tools as loaner items from the parts stores.

The heater core won't effect the A/C as they are not connected but if there was dye found in the drain the evaporator core has a leak as there is no other way for the dye to get there. It won't cause a wet carpet as there isn't a lot of moisture unless it's a very humid day. The leak at the condenser means it would need replacement as well.
As for replacing the evaporator core, yes you need to pull the entire dash out then remove the HVAC case and then split the case to replace the core. The issue with A/C work is that even a tiny leak will drain the system in a short time so it may not be worth it to do any other repairs if you don't replace the evap core as it will just continue to leak. As much as I loathe them you might try a test, remove the lines to the condenser core and connect them, then run a vacuum test and see just how bad the evap leak is. If it's not real bad you might try some sealer. Then see if it holds pressure, if it did you could replace the condenser core and see if it holds up for a while. I dislike sealers as they cause a lot of problems with A/C machines, if you try one be sure to put a label on the system saying that it was used.