The only reason to run 1/8 chain is because the cog or whatever you have laying around is 1/8. 3/32 isn't stronger, and the flexing as for shifting thing is a red herring. Pick up a 1/8 chain, it easily flexes side to side as much as it ever would on a single speed drive train; if you're going to throw your chain, it's going to happen regardless of whether you're running track chain.