Mike,
For our upcoming 4.0 release (later this month), we're integrating a few App/Website as Tab and Canvas features, so we've been doing a bit of testing in this area lately.. and hopefully, you'll like some of the new features you'll have at your disposal when using your website within Facebook as well.
In our development, we've been testing quite a bit of the configuration settings, and I actually think you'd want to have the following setup:
Site URL:
calendarised.co.uk/
Domain URL: calendarised.co.uk
Canvas URL (if using this feature):
calendarised.co.uk/ (or whatever page you want as the main canvas landing page)
Tab URL:
calendarised.co.uk/
When viewing your page in Facebook, FB actually will scan and intercept the calls for Logging in and Logging out so that it can automatically approve requests or 'see' the current user logged in. It's a benefit of being run inside Facebook, but I think you still want your app setup, in general, to be run outside of Facebook on your main site.
Try those settings, and see if you have more luck. If not, let us know, and we'll see what we can do.
Thanks,
Alex