UPDATE:
I've finally figured out a way to comprehensively fix this problem, though it took a lot of work and the creation of an Outlook 2010 addin! I plan on publishing this addin soon See below for the addon download. As far as I'm aware, though, there is no way to deal with this problem unless you install an addin to do it, because this is essentially caused by a bug in Microsoft Word's conversion of documents to HTML (which needs to happen before you send an Outlook HTML e-mail).

THE ADDON:
I have uploaded the source code of the addon that I had got round to developing when I originally posted this answer; I haven't had the time (or a copy of Outlook 2010 for that matter) to develop it further, so here's the disclaimer: this will probably not work at first because I can't remember where I was in developing it, but I know I got it to a proof of concept. I'm releasing this code under the GPLv3 so if someone with some development experience wants to try and get it working nicely with Outlook 2010, please do so and contribute your solution back (licensed under GPLv3) linked in a comment on this answer. However, I probably won't personally ever get round to making this a "finished" solution. The code is just to show you roughly how I did it. The addon is implemented in a Visual Studio 2010 solution, so you'll probably want to use that. Here's the download:
http://game-point.net/misc/OutlookQuoteFix.zip