When I did the heater core on my car I removed the entire dash for easy access.
Someone here has managed to replace the airmix actuator (that'* just above the heater core) in his SSEi, without removing the dash - he removed the glovebox and then cut the plastic ventilation tunnel behind it, replaced the actuator and glued the tunnel back together.
You'll need to do that too I think, and also remove the plastic cover below (the one above the passenger feet, it'* called the "insulation panel"). Then remove the airmix actuator (two bolts on top of it), and the plastic case covering the heater core (another two small bolts). The heater core is held by a small metal bracket - another two bolts. Then, remove the two water hoses that connect to it in the engine compartment, and the HC can be removed.
Here are two pictures I took while replacing the HC in my car:
Hope this helps