For the benefit of exasperated developers in years to come, here's how I fixed it. Firstly, jump ahead to the step 4. I'm certain I'd done that prior to re-installing, but it might be worth doing this step first to see if it helps. Failing that, do all this:
1. First I uninstalled SSMS, SQL Prompt and any other addons
2. Then I deleted all of these folders:
3. Then I re-installed SSMS
4. Lastly, I went into options, environment, keyboard. Pick "Visual Studio 2010 Compatible" from the download and MAKE SURE YOU HIT RESET. So far as I can tell, picking the drop-down changes nothing, it's only when you hit Reset that it changes everything.