How about something a little different?
Location - your choice from the following (all are in Antarctica):
79°44′24″S 108°13′12″E - South Geomagnetic Pole
83º50'37"S 65º43'30"E - South Pole of Inaccessibility (point on land farthest from coastline/ocean, accounting for ice shelves as well as continental land)
90ºS - Geographic South Pole
Frequency:
Anything with propagation enhanced via the ionosphere. Transmitter must be earth bound, in a fixed location with at least a somewhat regular schedule, and may not be located anywhere on Antarctica. (You may chase DX co-channel to them, though.)
Time:
whenever propagation is best

If you can simultaneously hear LW time, NDB and broadcast stations, 6 and 2 meter hams, FM radio and VHF TV from the northern hemisphere, with at least one station in each major band saturating a well-designed handheld portable radio's S/N ratio reception capability using only the supplied antenna, that would be preferred.
Also a quick side question. What conditions would be required for 6 hams to have a voice QSO (using only natural terrestrial propagation - no repeaters or satellites), such that...
• Their locations are: A = 90ºS, B = 90ºN, C = 0ºN 0ºEº, D = 0ºN 180ºWº, E = 0ºN 90ºW, F = 0ºN 90ºE
• Their frequencies, if not co-channel (full duplex wouldn't be possible if they were), are concentrated within 2x emission bandwidth of each other
• Minimum received signal strength is such that the S/N ratio is as high as using a large sensitive portable radio and several-foot tuned loop within the 3.16 V/m contour of an AM station away from any sources of electrical noise.