Interesting you mentioned the *spring* being soft.
Just got my MCN (US version) and on page 18 they did a brief sidebar of the K1300GT against the K1300S write-up.
They also complained about the spring being too soft on the K1300GT and preferred the ESA-I of the 1200 over the 1300 ESA-II system. They commented "That the rear suspension was oversprung and underdamped regardless of the setting, and the floaty bouncing sensation was even more pronounced on the GT." In the CycleStats section of the k1200S, they also gave the PANS to the "slightly floaty suspension feel" of the K1200S as well. PICKS for the K1200S were: Brakes, Instruments/Controls, and Attention to detail.
They didn't like the GT seat either, too low to accommodated short inseams and footpegs too far forward. Said the seat "Tilts forward too much."
Marks off on the "Backdraft from the windscreen" too.
Also mentioned, "Clutch shuddering with every start, which could easily be a peculiarity of the individual machine but, if so, didn't say anything good about quality control." Not addressed in the K1300 yet? I know, that rare Castrol oil no one can find in the U.S. is to blame (?).
"Tight twisties were not the bike's forte'" was also mentioned as the weight of the GT (100 pounds) over the K1300S they reviewed as well.
Fwiw, they listed Standard Maintenance as $824 labor + $174.06 parts = $994.06 for the K1300S. Yipes!