Martin, 'mode 2' IS does actually work if your technique is good. Remember, what it does is cancel out little movements at right angles to the direction in which you're pannng. But if there are movements which are too big for it to cancel, then the image will jump a little as the IS gives up and then re-engages.
I've never shot motorsports so I don't know from first-hand experience how useful it is. At a guess I would say not terribly useful, since from what I understand the sigma 120-300mm f/2.8 is a big favourite of motorsports togs and it doesn't have IS.
On the other hand I think IS is useful for nature shots. (I love the 100-400 IS, and I'm sure I wouldn't love it so much if it didn't have IS.) Not for moving targets, obviously, but most of the time most animals tend not to be doing very much; and the best time to capture them is often at one end of the day when the light may be a bit dodgy, and that's where IS helps.
If you want to try a 28-300 IS against your 35-350, .... oh, you know what I'm going to say.
Alternatively, given that you have a 28-105, you might find that the 100-400 IS complements it quite well. It's pretty much the same size and weight as the 28-300 IS, and it's still f/5.6 at the long end, but you have the extra 100mm to play with.