This might sound like a stupid question, but did you put the insulated part of the wires on the inside of the power jack?
And you don't need to actually wrap the wire through the holes, or around the terminals, just bend the wire into little "j"s to hook through the holes, then crimp them down flat with needle nose pliers and you only need a little bit of solder to hold the wires onto the terminals, just fill up the hole and get a little on the end of the wire till it's coated with the solder. The connection will be quite strong.
With that method, there shouldn't be too much bulk that would interfere with the protective cap going on over the wiring.
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