As wire length increases so does resistance, as resistance increases so does the temp.
But I don't think that was the problem
It sounds like a faulty bec to me. Do you have a voltmeter to determine the actual output voltage of the bec?
This is a weird one alright. You obviously had more current than the wires could handle, but that shouldn't have melted the extension to the bec.
I don't fully understand why you chose an hv servo if you were only going to send it 6v anyway? Were you just using a bec to lighten the load on the esc?
Perhaps it was a combination of too long of an extension and a faulty bec and both failures occurred simultaneously?