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The API for your timeline only goes so many tweets back, though. I think it's 3xxx tweets or thereabouts.

Which would be fine. RSS usually has a limited number of entries

Could always use the "download an archive of my tweets" thing as an optional way to backfill.

But is it possible to expose an API for your archive containing all your most recent tweets?

It will scale in most instances, if people provide the first x,xxx tweets, though.