It appears possible to remove the heater core by only removing the upper dash panel. This member found a way:
http://www.benzworld.org/forums/w163-m-class/1706293-heater-core-replacement-3.html#post5737839
In order to remove the upper dashboard, you first have to remove the instrument cluster and loosen the centre dash panel (with the radio and A/C controls). Then you remove the screw shown in the middle of RJV's 2nd photo, to remove the plastic cover to allow the heater core out. That member didn't find the screw under the foam gasket, so he broke the plastic cover trying to remove it.
I can confirm it is possible (only just!) to remove the heater core without removing the steel framed dash carrier, heater box and wiring harness etc., but it is still necessary to remove the upper
and lower dash panel and to unbolt the dash carrier at each end from the A pillars, from the steering column, transmission tunnel and the heater box. This task means the removal or unbolting of a lot of other nearby parts - heater controls, glove box, steering column, air bag etc, and even the wiper arms and wiper motor on the outside of the car.
This then allows the dash carrier to be pulled (i.e. flexed) far enough away from the firewall to allow the heater core to be pulled upwards from the heater box and to be squeezed out past where the bottom of the windscreen meets the firewall (back of the section which houses the wiper linkages).
If the dash carrier is not unbolted in this way it might be possible to remove the heater core but it, or the heater box, will almost certainly be damaged in the process and/or inserting the new and expensive heater core would be very, very difficult and the risk of damaging it, and/or the heater box is extreme.
See photo below :