A general average requires an imminent danger which the ship is clearly no in, since it's just stuck.
You also can't argue that they have to dump it overboard because of the costs that the delays will cause, because such costs are explicitly excluded in the 2004 rules on general averages [1]
>RULE A1.There is a general average act when, and only when, any extraordinary sacrifice or expenditure is intentionally and reasonably made or incurred for the common safety for the purpose of preserving from peril the property involved in a common maritime adventure.
While imminent danger is not used, the rule itself can only be applied when the jettisoning of cargo is essential to the common safety. This most often happens when the vessel is in imminent danger of sinking and needs to shed weight.
If the only way to get the ship unstuck from there were to jettison stuff out, and there were no way to otherwise free the ship (or safely unload the cargo) then maybe you'd be able to argue in favor of a general average, but given the circumstances that is not the case.
The ship isn't exactly stuck in antartica, so safely unloading, although expensive, is an option that would preclude jettisoning (and therefore the general average)
[1] https://en.wikipedia.org/wiki/General_average