We've discussed the ability to filter by submission metadata, particularly submission date and submitter ID. That sounds like it would help for pulling all patients last week. Do you have other filtering use cases as well?
One other thought: I'm not sure this is an official part of the API, but I think the ….svc/Submissions endpoint returns submissions in creation order (so that newer submissions come first). If you know you need the most recent submissions, you might be able to leverage that fact.
I also wanted to link to a few related discussions: