OK I'm sold in method #5!!!
I'm only missing one hole.
I put new solder on all 4 remaining holes.
Then I tried the wick on all and only got it to work on 1. Turns out I was pressing the iron tip too softly over the wick so the solder wasn't melting so easily. When I did manage to get it to melt, I might even burnt the pad.
So then I touched the tip of my iron on the remaining 3 holes and managed to get 2 nice little balls of solder out by tapping the shield over a towel that I have over the glass table. I didn't get the last hole because it may not have had enough solder in it so that I reached with the tip of the iron so I'll try again later with more time.
How do I clean off the guck over the pcb? I added some Flux yesterday and when I originally soldered the pins a while back and it's a mess.