I have this ongoing problem which is rather spoiling my enjoyment of my bassoon: the back pressure from playing it causes all kinds of squeaks and odd noises in my head! I guess it's air leaking through sinuses and ear passages and things. It's worse some days than others, and worse on the higher notes (more breath pressure). On very bad days I just have to give up. Has anyone else had a similar problem - and managed to find a solution? For instance, do I need to learn to manage a softer reed that would need less breath pressure? Or is there something else I haven't thought of?

I used to have that problem as well. I found several different solutions, although I have no idea why they worked for me:
I found that I was not breathing deep enough, as soon as I began to focus on my lungs filling up from lower to higher regions, the pressure in my head decreased. Second, I changed my embrochure to be much more relaxed, controlling the reed with only the tip of my tongue and a bit of my lower lip.
The last thing I found was that my jaw had built up alot of pressure while I played, as soon as I released that pressure, all the pressure in my cheeks and nasal passages released, and then all the sinus pressure released, leading to a pressure free head.