Should my pay be based on my DOR or the processing date according to S-1?

SGT (Join to see) - Somebody will have orders for your promotion -- the fact you are getting paid at your new rank at all means that somebody has those orders. They should be in your file at S1 but if they don't I'd ask your 1SG to look into it for you and/or guide you in your enquiries. Two reasons for this: 1-he/she will have a much better idea of how to chase them down, and 2-if you are acting under the direction of your 1SG, you are much less likely to make anybody mad at you. But either way, you'll get a copy of your orders and you can then look at your effective date.
Now as to the difference between DOR and EDOR - DOR establishes your seniority with regards to other soldiers of your rank, EDOR tells you when the army reckons you should get paid for it. They are often but not always the same date. In some cases the difference can be significant. I don't know why this is so but I do remember one soldier with a three month difference between DOR and EDOR.
Seven days is really no biggie. What are we talking about here? $55 or so before taxes? Call it $40 net. If $40 means that much to you go for it. Otherwise, I would just relax and concentrate on getting my stripes sewn on.

SGT (Join to see) iperms?

COL (Join to see) it hasn’t been uploaded

Your S1 should be able to get their hands on a copy of your orders. However like SSG London said, sometimes it isn't worth all the headache for around $50.