I think Mark I am in the same situation as you (with roughly the same requirements) so I would be interested to hear when you have decided on a solution.
Principally I want a system to track and log faults on a particular piece of equipment that is installed in most hospitals. Something that can log from the initial support call through assignment to the helpdesk or the engineering team and their actions/responses (In this particular case there is currently no requirement for the end user to have access)
From that I want to be able to generate a machine history report and
stats such as average time to resolution etc. Hopefully (given there could be multiple installations at one site) I would also like it if machines could be grouped as belonging to a specific site.
I have hunted around a bit and although it looks like RT could be bent into this shape I am not quite convinced it is the right tool.