For instance, it seems to me that advocates for direct democracy who try to persuade voters to vote for direct democratic parties are unlikely to succeed, but that widespread of VAA's might get us considerably closer to their ideal, and that they therefore should opt for the third strategy.

Berlin the city in which I live has a lot more tools for direct democracy than it had 20 years ago and I don't think that has anything to do with VAA's. It wasn't either about "persuade voters to vote for direct democratic parties". It's because we have developed a general consensus in Berlin that direct democracy is valuable that's shared among all stakeholders.