Hi Nick and welcome to the forums. 
Boxing in the extractor (allowing for ventilation) sounds like a good idea. That could make a difference though, I reckon it's the screaming router you should be more concerned with...
Taking smaller cuts or, larger cuts in numorous passes, is going to help you more so than running the cutter at a slower speed. The more the cutter is forced and made to struggle, the more likely it is that it will "complain". Regardless of noise, larger cutters should be run on slower speeds. I don't see how running a small cutter on a slow speed would necessarily affect the finished cut.
Another important point is to keep cutters clean and sharp. All I can add to the TCT vs. HSS argument is that TCT blades will hold their edges for much longer but, you can sharpen HSS more easily. HSS blades generally give a better finish when they're sharp but, that only really accounts for your planer thicknesser, not your routing.
I don't have any hands-on experience of the Woodrat systems but is it possble to box it in at all? I'm building myself a small router table at the moment. One of my reasons for doing this is that I can enclose the lower half and contain a lot of noise and dust - something you don't get with many off-the-shelf steel models.
Alternatively, you could look at insulating your shed - it will appear more costly immediately but it'll help keep the warm air in and may allow you to spend more time out there in the winter (...at least until Global Warming kicks in to fifth gear, anyway!). 
Hope this helps,
Olly.
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