@STumped has mentioned the two points that I was going to mention but I'll say it anyway - partly to completely agree, and partly to offer an alternative !
1. The bike definitely behaves differently without a pillion when the top box is fitted - for exactly the reason described. The wind 'eddies' behind your bike and clouts the top box from the sides, alternating left and right. The top box itself is on a sliding mount which is supposed to absorb some of this movement. Possibly the previous owner thought this was dangerous and did something to prevent that lateral movement. The movement is cushioned by oval shaped rubber inserts which are designed to give way to the sliding movement, but which cushion it.
Having said that, it goes away. When you get used to it (which doesn't take too long). My top box is on all of the time, and I ride with / without a pillion. I no longer notice it. My feeling is that you feel it and so you react to it. You tense up. Your reaction isn't anywhere fast enough, so instead of adjusting for the slight movement, you actually exaggerate it. You don't learn to react properly - you learn not to react at all. Loosening you grip on the bars helps. If you feel you are gripping tightly - try imagining gripping a thicker bar - so your hand is in the form of a grip, but is hardly touching - but ready to if you need to. I don't mean you should ride all the time like this. Just try it to reassure yourself that how tight you grip the bars doesn't make the bike ride better !
2. Pre-load. I was going to suggest the opposite. But if you need some.
One issue I found, moving from the ST1100 is that the front wheel feels as though it is really tucked under the front of the bike, and I found that to be very un-nerving at first. When taking it camping, two up, the pre-load would be wound up quite high - otherwise the suspension would bottom out when going over some bumps. I'd often forget to wind it dwon when we returned - and that felt very twitchy.
One reason is that when you increase the preload, it raises the rear of the bike from where it was before. This tucks the front forks silghtly so that the front wheel is even further back. You need the pre-load to be at the correct setting, but I found that if you wind it up too much, it makes the bike feel very twitchy - and it 'feels' less stable when in winds.
Again, you get used to it. And it stopes being an issue. Just like standing on a surf board for the first time. ONce you have done it a few times your muscles / reflexes / brain do not regard the movement as being anything that it needs to compensate for (or over compensate for).
Pan Weave was a phenomenon attributed to the 2004 and earlier bikes. Honda changed the way that the swing arm was mounted after that and is unlikely to be an issue on your 2006 model. THere are three type of mounting for the swing arm. From 2006 models, it has remained the same.
Top Box Rack. Givi E96 is good. Mounted either way round, but if you have the rear spolier/brake light it will fit ony one way.
I'll come back with a pic.
Get used to the bike. Ride with the screen down. Don't add to much pre-load - in fact try dropping it a tad. Tale off the top box of fit a pillion for a while. Get tyre pressures correct 42/422 psi. Check your tyres for being squared off. Check your wheel bearings. Make sure that the front wheel has been tightened in the correct sequence (ie redo it - I'll add a link after I've posted this).
Edits.
Animated sequence to show the correct procedure when installing the front wheel into the forks of a Honda ST1300. The right hand side of the bike is the side with the brake lever. Left is the clutch lever side. This is the convention used in the Honda manuals. The video and the photo below...
www.st-owners.com
The Givi E96 rack. Mounted this way it looks as though the front gets in the way of the pillion - but it doesn't.
However, when I fitted the brake light spoiler, I turned it round the other way and I sawed that loop that seems to protrude off.
