I'd expect that the ideal carbon-capture strategy is to grow a tree as quickly as possible (ie: a fast and easy growing wood like poplar, or maybe bamboo), and then probably bury the wood deep underground. If any bacteria eats the wood, the CO2 gasses should remain trapped there.

The expectation that permaculture is actually the best carbon-capture strategy is... strange. Trees eventually die, and at that point: their captured carbon is eaten by bacteria, turned back into CO2 and released into the atmosphere. There is a degree of carbon-capture with natural forests, but they aren't explicitly designed for carbon capture.

--------

Now if you think there are other benefits of permaculture, then of course, that's to be discussed. Maybe it'd be more beneficial to the wildlife (more room for predators / prey to roam the lands), and possibly beneficial for other reasons in the long run.

But if we have a specific goal (ie: carbon capture), that's easily measured and easily quantified, then frankly... modern science is the best approach forward. We should measure various methodologies, and then compare them. And then incrementally engineer a solution over the years based on the target quantifier.