I always used the BT020 F rated tyres on my 1100s. They were always pretty good and reliable. My first tyres were the exedras, and the BT020s were not available in their early years for the non-ABS bikes. As soon as I was able to fit them I went to the BT020 F rated, and they were a revelation. Very odd feeling for the first mile when I started riding on them - the more rounded profile made it feel as though I was balancing the bike more than before when I was on the straights, but the cornering was always a smooth progression.
This feeling disappeared once I had got used to it, but I distinctly remember the contrast. In those first few weeks of riding the radial 020s rather than the cross-ply Exedras.
The 020 would develop a significant square profile on the rears towards the end of their life, wearing down the centre far earlier than the sides - so there was a period when leaning over demanded a bit more positive input to get over the 'corner'. Nothing to do with riding long straight roads. But a new set in the Alps and Pyrenees for our frequent long touring holidays were superb.
My favourites have been the T3x series of tyres - currently the T32. Predicatbale tyre wear and fun all the way to the wear bars. You need the GT version for the heavy ST1300.
Here's a link to Bridgestones Tyre size table for the T32 - you can check id the tyre is made for your size. It's a pdf file, so check your download folder once you have clicked on it.
Check the suspension, and air pressure. The ST1300 requires 42psi front and rear. I think that the 1100 was different. (36/42 ??) Get your pre-load right where it needs to be, and remember to adjust the damping by adjusting the small slotted screw at the lower end of the suspension unit. It can be accessed therough a small hole in the large footstep bracket on the right hand side. If your bike is rebounding more than once - boing boing boing - then it needs to be set harder. That bouncing produces are reciprocal squash rebound squash rebound behaviour in the rear tyre.
Tired wheel bearings that have developed a tiny bit of play - or the incorrect bearings - can make the steering feel uncomfortable, particularly when leaning over. My very first 1100 had this problem - as an old rider returning to motorcycling after riding with sidecars 20 years ago, this made me very nervous when cornering - yet I couldn't feel any play in the bearings. I eventually thought that I felt something after putting it on the centre stand, supporting the bike with a platform kjack under the sump and tying the handlebars on full right lock. Then grabbing the wheel pushing on the top, puliing on the bottom and vice versa - I thought that I felt a little movement. Still wasn't sure, so I replaced the bearings all round. That solved it.
Also check the the fit of the front wheel. There is a correct procedure to follow. If you don't follow this procedure to the letter, then you can end up with a (dangerous) twitchy front end.
This is becasue it is possible to have everything tight, but the front wheel is able to slide side to side on its axle. Not much, but enough. The reason is that the axles has to pull everything together from the right hand side of the bike. It clamps the bearings and spacers tightly together against the right (brake lever side) fork leg. If you tighten things int he wrong order, then you cannot clamp all of the front wheel parts together, which makes the wheel free to move side to side on the axle.
Watch my animation a few times. I've exaggerated the movement to make it easy to see what is going on. Its created in a high resolution, so looks better full screen. ALso not the picture of the spacers - which many seem to get the wrong way round (easy to do) or on the wrong sides (not so easy, but it doesn't stop it from happening).
(1) Article [13] - ST1300 - Maintenance - Front & Rear Wheel Install and Front Axle Animation | ST1300 Articles | ST-Owners.com
I know this thread is about the 1100 and my link points to info about the 1300. The detail is a bit different. The priciple is the same.