Update on the above. We married in Colorado last week! I'm now back in the UK, and we're getting things together to start the visa application process. My wife is taking my last name (her choice) and is in the process of changing her legal name, so we can start the paperwork with her married name. This should take around 2 weeks to process.
My wife will also be renewing her passport with her married name (and as the photo is now around 7 years out of date). While this should only take a month to process (based on previous/family experience), it could hypothetically take up to 6 months. Does my wife need her new passport for us to start the visa process, or is the passport only required for entry into the UK once the visa has been (hopefully) issued?
Any other advice on this aspect greatly appreciated!