Drywall newb and an old guy to boot. :D

Hey all,
I've done very light patching and such with fairly good success in the past despite me being as slow as a turtle when doing it. I had some water damage from a leaking toilet valve. The problem has been fixed, but it left an ugly discolored patch of ceiling right at the front door area. My wife finally nudged me to do something about it, so here is what I did:

1. I used an angle to mark to the outer areas of the damage in the attempt to make a square or rectangular area that would be easier to make a patch for.
2. I cut out the affected area and confirmed that no mold was growing rampant in the ceiling.
3. I got a full sheet of drywall because they only precut 2'x2' portions and my cutout was 26'x22.5'. In retrospect, I should have made an effort to see if I could cutout the damaged piece with the existing 2'x2' precut piece I had, but I didn't.
4. I spent way to much time adjusting the hole to fit the patch I'd cut from the full piece of drywall
5. I put the furring strip up on the side that didn't have a stud
6. I screwed it in and the existing drywall seems bowed down where my new piece is nice and flush. It's flush on 3 of the 4 sides and has a maybe 1/4" to 1/2" bow in adjoining drywall. I'm not sure how to address this.

My first thought is to put a shim or two under the patch on the side where the wall bows out to match it as closely as possible and then just continue with the repair. From what I read, I should pull out the entire section that is bowed, but that is beyond my physical, mental, and spiritual capabilities at this point. This little patch job almost did me in. I'm hoping that I can fix this good enough to pass muster without having to pay someone to come redo the entire section. My plan at this point is to use a shim or two to raise the section next to the bowed section until it gets as close as possible w/o going over the existing drywall, mud it, clean it up, make an attempt at matching the rosebud patterning, and paint it. Not sure if there is a better way, so I'm here for some advice. Here are the pics:




Thanks in Advance for any advice,
Jeff