I know those big 1200s in the right hands could perform. Had a buddy with with the R1300RT. His only gripe was that it was governed at 135 MPH max. Another with a R1200GS ADV was one of my regular riding buddies. As you can see, he liked to give it the beans. Both loved their bikes and would take them with our sportbikes.
Forgive me. Whatever these stubby nosed BMWs are. I thought they were 1300s. I don't think he was lying to me as I don't think he was ever afraid to top a bike out, but his bike did appear to top out or be governed to 135 MPH. If it wasn't governed, maybe the top gear was so tall it couldn't push the big fairing?
So in the end I bought a Honda VFR1200X Crosstourer, which has a 21.5 litre tank. I regularly get 200 miles to a tank, or just about 250 if I ride at a steady 70mph for most of my 50 mile commute to work (which is 90% motorway). It's great bike, shaft drive and I have the DCT version too which makes riding and filtering a breeze. It's heavy though.
I'm thinking of downsizing though to a Honda CB500X but am unsure as to how good it is on the motorway.
Would still be useful if I could somehow sort bikes as to the best mileages between fill-ups!
I'd think the NC700x would be the logical choice if you were looking for something a little more nimble, but along the same lines. It's the MPG king of the hill, along with the Triumph Tiger 800, on average.
Another great bike, but with some spirit to it, would be the FZ-1. Ride it the same way you mentioned and I don't think you'll be disappointed.
The longest tankful recorded here for my 1995 R1100RT is 424 km (264 miles) from 25.2 litres, with a couple of others over 400 km. R1100RT (BMW R1100RT) | Fuelly
Sadly I think everything recorded there is pretty much short distance city work. Back before I started using fuelly I often went from Wellington 880 km to just north of Whangarei with a single fuel stop at Tokoroa, basically exactly 440 km (273 miles) for both legs. And never going slowly :-)
I once toured 2-up with another couple on an F650. While following them around slowly (100 km/h) I got 535 km (332 miles) from one tank. It's extremely rare for me to ride so slowly on the open road, but that's what the bike will do.
I'm sure the newer ones (1150, 1200, 1250) are more efficient.
More recently I've just bought a CRF250R Rally and my sister an NC750x. Will be interesting to try riding together sometime. My first tank I used 3.5 l/100km but that's new tight engine and some increasingly thrashy riding to break it in. The 750 can supposedly get that kind of economy too, but has a 14l tank vs my 10l. Fuelly shows most of them averaging 3.8 or 3.9 l/100km real world, which probably translates to 450 km (280 miles) maximum practical.