I'm fairly certain that it would work just like shares.
At the point a company is first created it's shares have zero value and so it's founders pay no tax when they receive them. The fact that they gain value later has no bearing on that situation.
Of course, creating shares at a later point in a companies life (when they may have value) does have tax implications.
Thus, any coins that were mined before there was any value you shouldn't need to pay tax on.
I think you're right(ish), with one caveat that I think you understand, but this time last year I would not have...
If you ever sold them, and long-term capital gains should apply, you would still owe the long-term capital gains tax on the proceeds from the sale. So, subtract your cost basis (which for THE actual creator of bitcoins is arguably more intensive than average miner who merely creates bitcoins), subtract that which has not been (depreciated?) on any other gains, and pay tax on those gains from the proceeds of the sale.
At the point a company is first created it's shares have zero value and so it's founders pay no tax when they receive them. The fact that they gain value later has no bearing on that situation.
Of course, creating shares at a later point in a companies life (when they may have value) does have tax implications.
Thus, any coins that were mined before there was any value you shouldn't need to pay tax on.