Hmmm... That's weird. It should run just fine on one. I know mine does, and has for the last 15,000 miles (I'm running a turbo computer which has the timing curves set up for a slow burn single plug head which means if I run both I get pinging). I'd look into the coils and wiring to make sure everything is in good shape. Most likely you have 1 half of each coil is bad but the good halfs of the coils are on opposite cylinders, so when both are in you have one good plug on each cylinder, except it's the drivers side on 2 cylinders and passenger side on the other two. But if everything is working right, it'll run on one coil just fine (except it will only fire the primary (passenger side) when cranking, so it shouldn't be able to start if you disconnect the primary side coil).
As for being able to run all 8 on premium - I'd say that's a good possibility. Really you just have to try it and listing for pinging. If it does it without pinging, you're good. If it pings, disconnect the driver's side.