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But this reduced alkalinity is caused directly by the ocean's CO2 absorption, not temperature, right?

Yes. It is caused by absorbing CO2 faster than ocean circulation can offset it by dissolving lime from the bottom of the ocean.

If the CO2 rises and stays raised, in a few thousand years the Ph will go back to its old value.

If we wanted to solve this problem, one of the better ideas is to crush limestone and dump it into the ocean. As a powder so that it dissolves before it can sink.

This is brilliant and I feel foolish for never having thought of it. No one is going to stop someone from dumping barges worth of powdered limestone into the ocean; and one with the means could action this immediately.

How much limestone do we need?

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