As of about two hours ago I've had confirmation that the Chinese embassy has granted me my visa, after a couple of wobbles with the application due to needing to prove more clearly that I really did need a dual entry visa (the second entry is for my Mongolia-to-Lima flights, which takes me through Beijing for a couple of days, along with London and Miami - for those keeping track). This is a huge relief as I can't afford to lose any more time with getting visas sorted.
A small issue with my application for Azerbaijan, in that the form asks where your passport was issued (answer: the UK), but the real question is "write the details of the issuing authority as printed in your passport into this box" (answer: IPS). One re-submission of the paperwork later, a bit of a faff with a printer (things with a paper path are evil) and a lot more of a faff with a scanner later and the paperwork is now all with Travcour. An exciting 45 minutes, but it means my passport will be with the Azerbaijan embassy tomorrow morning.
In excellent news Dragoman have managed to get some paperwork which should help speed-up the processing of the Uzbek visa, which hopefully means that I'll still get everything back in time and I can stress slightly less about the visas and get back to sorting the storage of boxes, which is what I have been doing otherwise today.
One visa down, three to go.