Well, my friendly electrician returned today and found the break.
Located in a junction box, one of NINE, yes 9! found daisy chained together in the attic, the Romex aluminum wire had some fine scorching.
So, on the bright side we didn't need to tear through any walls, not yet anyway.
Reducing the load on the circuit was a must, so I completed the install of the LED Lights.
I chose the Ecosmart 6 Inch Bulb LED. With a CREE LED it's the equivalent of a 65 watt bulb with only a 9 watt draw. Much safer and energy saving as well.
The install is however not exactly drop-in. But it is close, especially considering I could do it.
First remove the 65 watt bulb.
Next remove the trim by pulling out the two springs from the slots.
Next unscrew the wing-nut holding the plug in place and pull the plug holder out. Remove the plug from the holder by pinching the two black plastic pieces on the plug.
Next, screw the LED bulb into the plug, expand the three metal wings on the LED Bulb (I found the second position fit the cans best).
Next push the bulb up and twist so the three wings engage the canister, and you're done.
When everything was going well, this took about 5 minutes per bulb. When however I encountered miss-cut holes for the canisters hidden by the trim requiring re-seating the entire canister and trying to make it not fall out of the ceiling completely, stripped wing-nuts keeping the plug holder in place, and other sundry idiocies the house refurbishment monkeys performed, it took longer and enhanced my vocabulary considerably.
The LED lights are quite pleasing to the eye, perfectly dimmable and an easy replacement. Considering the power saving and safety benefits of having them on that circuit it was a worthwhile upgrade.