If you want to save money and use an excellent sport touring tyre then forget Michelins and get a set of Avon Storm 3D XM. I use them on my R1200RS and they are popular with Hayabusa riders. Last pair were £190 fully fitted from Protyre in Gloucester. Work well in winter, really well in the Pyrenees and last well.
Dunlop Roadsmart IIIs really suit the K16GT - great grip wet or dry, nice steering and 6,000 miles per set. No heavy duty version, the standard ones have quite a stiff chassis, absolutely rock stable flat out with passenger and luggage.
Pretty much anything is better than the Bridgestones.
I would only recommend Dunlop Roadsmart 3 - and, after I put a few ore miles on them, maybe the Michelin Pilot Road 5 GT. The Dunlops have had the most consistent performance throughout the tire's lifespan out of anything I've ever tried, in 16 years, on any bike. I highly value that, as I hate tires that are amazing for the first 2000 miles, and then turn into various degrees of rubbish for the next 3000 - 5000 miles.
The Pilot Road 5 GT shows small improvements in handling, comfort, precision over the RS3, but if the wear is not as consistent and predictable - I will switch back to RS3s. Time will tell - in the meantime I have no reservations in recommending the Dunlops.