Either the welds are funky, or you're just hitting a resonance when you're warming up your motor. Does everything vibrate and get blurry before it breaks?

The solder of choice is sta-brite. Available from Tower or from finer hobby shops everywhere. The flux that comes with it works very well but is awesomely corrosive, so wash it off after the joint cools. Strip a length of copper wire and you'll have a pile of strands of copper with which to wrap the joint. It'll be as neat as you make it. It'll be good to use steel wool or a Dremel wire brush to remove the plating before wrapping and soldering. A torch works better on such large joints than a soldering iron or gun. Might be better to take off the wires and bolt them to a sacrificial board before applying heat.