If you need to travel several days after you submit your annual non-imm. docs - can you have the review completed the next day for an extra fee?

No, the application must be proceed at regional HQ. 

You need to get a re-entry permit for your under consideration stamp. 

so once you get back, you can just show up when-ever and complete the review? (assuming the original report-back date happened when you were overseas)

Edited March 28, 20188 yr by pkspeaker

1 minute ago, pkspeaker said:

so once you get back, you can just show up when-ever and complete the review?

You will have to return before the report back date on the under consideration stamp since that is when the re-entry permit will expire.

There is no addition review.  You go back to get the one year extension stamp after it is approved.

19 minutes ago, pkspeaker said:

so once you get back, you can just show up when-ever and complete the review? (assuming the original report-back date happened when you were overseas)

If you are unable to return within "under consideration", you need to start over, recommend getting new visa while abroad, entering after the period will only give you an visa exempt entry for 30 days. 

In this case don't bother paying for a re-entry permit.