You've already got the document mode sorted. Does that not solve the problem? It usually does the trick.
The browser mode shouldn't need to come into play, as it doesn't affect the rendering at all; it just changes the UA string, so it shouldn't have any impact on the page layout.... unless there is something in the code that tries to do a browser-specific hack by looking at the UA string.
If you have got something in your code that does that, then that's where the problem is and you should probably fix it. (using the UA string to affect page layout is generally frowned on as a bad practice anyway; there are usually better ways to do it)
If it's Telerik itself that's doing it, then I would imagine they'd have already been forced to find a fix for it (IE10 has been out for a while and they'd have had other users complaining), so you may find that updating to the latest version will solve the problem.