Well, I'm back from a weekend trip and I thought I'd load up the page just to remind myself of where I'd got to with this. Lo and behold! it worked!
I loaded up the app (
http://www.my.site/myapp) and got the blank rails welcome page. I tried the controller (
http://www.my.site/myapp/test) and it outputted some text saying "this is a test" (which is what I told it to do), so all seems well. I'm going to try doing something that actually accesses a database next, I'll post here afterwards.
I'm guessing the delay in this working is due to the FastCGI process needing to restart (??)
Well, for now if you're trying to deploy a rails app, follow my instructions above, give FastCGI some time to restart (or pester support

) and post your results here!