Can this piece be installed upside-down/backwards or is it supposed to go in only one way? I don't think it is quite...

Try this: (pay close attention to the pics for the location of the component) http://www.mauron.net/iphonerepair/ As unlikely as it may seem - this actually worked for me after losing signal following a screen replacement - and I had searched and tried EVERYTHING else first (at least a hundred different pages of tutorials, guides, videos - you name it). If I hadn't done so much reading though, I wouldn't have come across the solution, but it was a needle in a haystack. Frankly I am totally astounded that the fella who posted it was ever able to locate the problem; the piece is REALLY tiny and I never even knew it was ever there, much less that it was missing until I had tried everything else under the sun. I finally stumbled onto his post in a comment from another fixit page with hundreds of people with the same problem and no fix. I had been so careful, I really didn't think that could be the problem, but when I got out a magnifying glass and studied the mobo, sure enough that little inductor was missing!...

The best place to get the answer to that quickly would be the wiki at Geekhack.org or Deskthority.net - input device enthusiast forums. If they don't know what keycaps to fit and where to buy at the best price, I doubt anyone does... =)

There is a TEENY TINY inductor on the motherboard which is apparently very easy to knock loose of the soldering and therefore breaks the antenna circuit if is dislodged, I would look at that if a software solution is not helping. Most of us doing first time repairs were entirely unaware we'd lost it most likely when we first removed the motherboard's last screw under the "Do not remove" warning tape. I had no idea why my new screen worked so beautifully but I had a whole new problem of "no service"! I tried everything and found no solution until this (thankfully someone figured out what no one else had) Check for this component either missing or loose and/or damage to circuit traces in this area. Also check that the dock connector piece hasn't come apart at the seam and lost the spring loaded pin which is supposed to contact a small pad on the motherboard - too tight screws or the wrong screw can cause the board to bend just enough to break that contact because it lifts away from the pin also.