Well, the first thing that popped into my head were all those references that saidar and saidin are the combined force that turns the Wheel of Time. So they must encompass it in some way, I imagine maybe like in an intergalactic pool or something with a current that turns the Wheel?
This would mean the Bore was driven through the True Source. I don't remember right now, but doesn't the short story of the moments before the Bore was drilled show 'Meiran' thinking that they found a new source of the power, beyond the One Power? Perhaps this fits if I remember that correctly. I'm typing as I think here...
Anyway, maybe it's just as simple as using the male and female halves of the True Source together to patch the hole in itself? It certainly would be a significant way to fulfill the duality theme of the series and explain why using saidin alone was a bad idea.
I'm not married to this hypothesis, just following your advice and throwing stuff out there. Good topic...