I'm pretty sure all tweet IDs are in a single global ordering, so "1 week 
ago" is the same numerical ID (for the since_id) param for every user 
account.

So you could post a single tweet (or similar) every day and use this to 
build a "date to ID" mapping over time... then you'll know an ID to use to 
indicate "1 week ago" for any given date past when you started (and it's 
pretty simple to build a historical table) - then you can experiment with 
using the user/timeline API with "since_id" (and "max_id" too if needed)

Don't know for sure it would work, but from what you've explained so far, 
that's the sort of thing I'd experiment with first...

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T

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