My recommendation mount an Avon Storm Ultra II on the front in the 110/80/18 size along with a Avon Azaro 150/80/16 on the rear. Your not going to get big mileage on the rear tire, you will get somewhere between 6,000 and 8,000 mile from it, and you can get considerably more from the front. This will give you a baseline of how good your bike can be with good tires. The Avons will give you quick turn in, precise steering, great grip and very good feel.
I've been riding ZG1000s for 21 years, I've averaged over 30,000 miles a year in that time, I've gone thru a lot of tires. This combo is as good as it gets on the C10.
If you feel you need more mileage from your tires fit your bike with the same Avon Storm on the front and fit an Avon Venom bias ply on the rear. I've ridden this combo and it feels pretty good. I can detect the rear steering a little slower but most riders will probably not feel this.
You can run Goldwing size tires if you are comfortable with heavy slow steering, you will get more mileage from them but at an expense I could never deal with or recommend. God luck with your choice and enjoy your Concours.