HI Tim
some thought as I like you would like some clarity on this one, it's probably something many of us have wondered about.
the bike having been run with the pistons being transposed I would think you would put it back together with them still transposed, don't think it matters for pistons but rings would probably like to stay in familiar territory, when you get barrels re bored they generally ask for a piston, one being suffice, so pistons are not regarded as pairs, rings on the other hand will bed into whichever cylinder they encounter first (I think, other comments more than welcome.)
The arrow thing, I pondered this often, on the one hand pistons are not symmetrical in all dimensions, on the other hand how can they not be symmetrical front to back if the gudgeon hole is central, again more enlightened comments welcome.
If it was my bike I'd put a new set of rings on then put the pistons back anyway that makes sense to you providing the bore is OK