So, I stripped the shrinkwrap and unsoldered the bullet connectors, and extended the wires. There were a dozen of the things to do, so I did one first to check for fit, and then did the remainder in a batch, assembly-line style. I made them a tiny bit longer than they needed, so that we would have some wiggle-room (literally) for the ESCs. Next time, I'll try making it an exact fit.
I didn't try reusing the bullet connectors... they were kinda messy on the outside after soldering. I wonder if there's any way to clean solder of lots of pieces at once? I was also surprised at how heavy a dozen connectors full of lead solder weigh. I tried using the minimum possible solder on the new connectors. It made it a bit more tidy as well. It seems just as strong... I wasn't able to pull it off by tugging at it.
I took photos... partly because I thought it might be useful for someone not super-experienced with solder, but mostly because I thought they would look pretty cool.
Cut all the wires to the desired length, strip and tin the bullet side. You don't need much solder, since these are being placed in the connector cup. Just make sure the wires are saturated. One of the previous posts has some details about using the board to hold the connectors. Strip the insulation so that the exposed wire is just as long as the internal connector cup.
If the solder sticks to the alligator clip, touch the soldering iron to the outside of the clip and it will come right off. Don't tug, or the two wires will come apart.