Well if this isn't an intrinsic design problem with IE10 you could try an alternative like WOT (Web Of Trust). Not sure if it works with IE but it does the same sort of Avast WebRep thing. I have both as there was a problem with WebRep and the Opera browser which I was trying out a few months back. I installed WOT on Opera and then when I installed an Avast update and WebRep started working again I kept both and also installed WOT on Firefox too.
You should consider going over to Firefox as that makes customisation like this easy. Even Opera, which isn't as customisation friendly (or generally as well designed IMHO) as Firefox, allows you to reposition the address and search boxes meaning you can choose where your toolbar icons are placed, if not their order.