they will not allow us
Article IV § 2 states: No acts or activities taking place while the present Treaty is in force shall constitute a basis for asserting, supporting or denying a claim to territorial sovereignty in Antarctica. No new claim, or enlargement of an existing claim, to territorial sovereignty shall be asserted while the present Treaty is in force
That only applies to countries that has signed the treaty. Which we won't. Anyway, non of the nations have the right to deny our claim either. Also, if they disagree with our decision they can't do anything since according to the treaty, no military activity is allowed on Antarctica. I don't see what could possibly stop us? (except for money)
hmm
you made a point there
but it's Antarctica, it's -70C

who would want to live here?

altough, yeah, nice temperature so our miners don't overheat

but we'll have a hard time acquiring free electricity
In the coldest place on Antarctica the average temperature is -55°C. The costal areas however is much warmer. During the winters the average temperatures is around −18 °C, while during the summers it's about 0°C, and sometimes even more.
Who would want to live there? Well, people who feels this is a cool concept and people who have no future in their current countries would probably at least consider it for example.
And no, we would not have to worry about miners overheating!

The electricity, as I've said earlier, we'll get from solar power, wind turbines and power buoys, and with the right amount of them they should be able to support us.