And the ever-useful "The True Size Of…": https://www.thetruesize.com/#?borders=1~!MTU1OTcwMjU.MTI5MjQ...
I think you're overstating the difficulty given that population distribution.
And those two large splotches on the map representing Calgary and Edmonton and with most of the population pretty close by, they're only 282.6 km apart.
A 10cm^2 cross section of aluminium between them would have a resistance of 7.3 Ω, and even when bought from the first random supplier I found on Amazon that would only cost about €14m:
https://www.wolframalpha.com/input?i=resistivity+aluminium+%...
https://www.amazon.de/-/en/Aluminium-Square-Solid-Material-S...
https://www.wolframalpha.com/input?i=282.6+kilometers+*+€5%2...
It would be about 12% of that price, €1.7m, if bought at bulk rates: https://www.wolframalpha.com/input?i=282.6+kilometers+*+10cm...
At 1e6 V, 12.7 GW is 12.7 kA; I^2R losses over a 7.3 Ω link for that current is 1.18 GW: https://www.wolframalpha.com/input?i=%2812700+amperes%29%5E2...
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But even without any of that, there is one very important point you've overlooked:
Alberta has already got a power grid.