Could anyone who has covered such distances on a 4s (or predecessors) fares over the longer distances with regard to comfort and handling?
Not an audaxer. Bought my Tk mainly because for some years I had a twice a week 2x30 km commute. Longest stretch I have done on it is probably around 120 km with two panniers and a bar bag.
The steering isn't twitchy at all, but not sluggish either. Once I am rolling it takes no effort at all to steer it. I always find it a very relaxing ride when I am on my Tk.
I also find it extremely comfortable with regards to road buzz. I ride in the hoods (Campagnolo) almost all the time, with some riding on the tops. 28 mm tyres probably helps a lot when it comes to comfort. A good fit is probably just as important. I had one of those computer-laserscanner aided fits, which actually proved really useful.
My setup is; 36Hx3 wheels with Mavic CXP33 rims, dynamo hub, Brooks B17 saddle since my tops are roughly at saddle height, Campagnolo Ergo shifters. Upgraded from Campagnolo square taper to UT crank. Was surprised to find it improved the "feeling" of the bike considerably giving the same "oneness" with the chainset as on a fixie. A Tubus Logo steel carrier also proved to be a great upgrade, since its extreme stiffness prevented the tail wobbling I experienced with the (admittingly overloaded) lightweight Tortec aluminium carrier I had before.
All in all a fun bike to ride, even with loaded panniers. Should I ever need a new audax-like frame, the Kinesis UK 4S would be my first choice without any doubt.