oh my ! What we do for neighbors ?
Traditionally ( not that this matters ) the channels are left as is, and the slipcover is allowed to fall into those areas. Was it great ? Not unless it was un~sat~on. Traditionally, wood is left exposed.
Not that you can always afford to mess with neighbors, but as long as there isn't a feud now....no harm done ?
Big one for me, is I never mess with the furniture itself unless I am assured it has zero value as is. I cannot say I have never ever patched a hole or draped muslin over a rough spot, but it's rare and it's always messy looking when I am " finished ". It still looks unfinished when I consider myself finished. I tell them the price to do that is zero, about it's value. That's me.
Channel chairs are already ( usually ) poorly symetrical, it would be very difficult to make them symetrical externally. My back hurts just picturing you leaning over this......