One little addition, just made it and helped tremendously. At the engine bay, loose completely the tiny screw holding the in/out flange for heater core as already mentioned. Mine screw sat in there, but obviously was undone - no need to remove. Then, very important step!!! not described yet - peel the rubber boot around the flange with screwdriver and pull the flange out towards the engine. It will likely move an inch or so, but once the rubber boot no longer is wrapped around the flange, the tubes inside will stop bouncing back towards the tubes of the heater core.
Before doing that, I was prying the tube connection as AnchorsAweigh described and of course scuffed the ends a bit, and barely separated 1 mm. They were bouncing back in. After I peeled the rubber boot infront I shook a bit sideways and out and to my surprise when I went to fight again under the steering wheel, they were off already, with tube seals now out. It took just a tiny effort to get them off completely and the core slid right out with slight tilt of the front downwards just before it completely got out. Actually, you may find out you won't even need to pry tubes at the heater core beforehand, as the connection after taking the clamps look rather loose.
You can see on the image below the groove of the flange where the rubber boot was. Another benefit of taking the coolant connectors off is you can blow off the coolant from the heater core to prevent leaks inside.