Well. Let me try answering. I am no expert and just about understood some stuff after reading numerous posts here late into the night most likely due to sleep deprivation.
If you have filed taxes returns, you can get a consolidated tax report for the last three years from the IRS faxed to you (not sure if that applies if you have paid taxes but not filed returns). This takes 5 minutes. That is what I used along with my 1040 forms submitted. It was funny but this was the first time I saw the amount we workers contribute in general - a whopping 150k.
In any case, I don't see why submitting a document after the interview affects or delays a case. After all you have done your part honestly and quickly. Do keep proof of what you submitted along with the date.
Going to the INS office for a status update of the case, may or may not help depending if anything has actually changed.
More often than not I feel there is little that has changed. Which could make the trip wasteful. What is even more disheartening is that you have to spend practically the whole day - an hour outside in the cold, a good 4-5 hours awaiting for your turn and watching Jurassic park (there is cable nowadays - a sign that they are becoming customer oriented albeit slowly), and 5 minutes or less at the window.
An alternative or rather a parallel course of action is speaking to your congressman. I have done that too and am awaiting a response.
About AP, this is needed if you want to travel. You can get one after the interview too. Infact you have to if you are going to travel since your case is pending.
You will get replies - infact I think this forum is most helpful.
Very often the questions have already been answered and it is just a matter of going through innumnerable posts and identifying what pertains to you. That's my take.
The site is also well managed and fast.
Hope this helps.