TL;DR - I fitted my bike with a radial tire (Pirelli Scorpion Trail II) on rear and the stability, comfort, and handling have improved markedly.
If you decided to read on, I thought I might start by giving some context for the discussion:
A year ago a buddy and I flew down to Florida in the heart of winter to do a long weekend riding from Tampa down the Overseas Highway to Key West. Since we flew down we both rented rides in the Tampa area. Harley dealers were the only thing we could find, so we both ended up getting different flavored Sportsters for the ride. While trying out one another's bikes we agreed they had very different handling and comfort characteristics. It wasn't just the suspension or the seating/handlebar configuration, something else was at play which made one model much better handling, more stable, comfortable, and just better mannered and more confidence inspiring. Eventually we pinned the difference on the fact that one model had been fitted stock with Michelin radial tires, while the other still maintained the traditional bias-ply. The subsequent research I did seemed to indicate that Radial tires are slowly but surely taking more of the market for motorcycles; most legitimate sport bikes already use them and every year more bikes in other categories begin to use them as stock rubber.
I won't go into all the reasons you want Radial tires here, but if this interests you do some research. Sufficient to say that I was very compelled to get a pair of these for the V7ii Stone next time I needed new tires. That day finally came, and due to a lack of options for radials on both back and front, I actually ended up settling on a radial rear and bias front setup (which is fine, but radial on front and bias on back is not recommended).
I bought a set of Pirelli Scorpion Trail II tires in the original stock sizing of 100/90B18 (Front) and 130/80R17 (Rear). Mounted them this past weekend and got out for 100 mile ride yesterday. The difference is night and day. The stability on highway over rougher surfaces/concrete is so far improved, as is the quickness entering a corner, cornering stability and just general comfort. The Pirelli Sport Demon tires this bike came with were very decent tires, but they are bias ply. From now on when choosing tires I am certainly going to exercise a very strong bias, towards getting radials.