More specifically, fast forward to 2080, when any college kid with $200 to spend (in equivalent 2012 dollars) can purchase enough computing power

If computing power is that much cheaper, it will be because tremendous resources, including but certainly not limited to computing power, have been continuously devoted over the intervening decades to making it cheaper. There will be correspondingly fewer yet-undiscovered insights for a seed AI to exploit in the course of it's attempted takeoff.