I think your split/groove/fill method is probably the easiest for the cord running in both the center post and the legs.
My question, though, is with a hole down that center post, how are you planning to attach the legs to it? Like you said, it's pretty thin. Are you planning to use some steel brackets surface mounted that hide inside a mortise in the leg, perhaps?
I can't see traditional joinery working in this case unless that center post is thicker than I think. Maybe I'm just worried too much, but it looks to me like a mortise/tenon joint at the leg/post would only be able to penetrate 1/2" at most. Is that enough, really?
Oh ... about the cord run through the leg. I'd do it on the inside, myself. With careful grain matching, the leg's own shadow should make the seam pretty much invisible. In fact, don't fill a slot, lay a full-width piece overtop and you won't have an issue. You could even get fancy and miter at the corners so there's NO seam at all.
And where do you think you've got the time to make sawdust? Don't you have another machine to restore? :P