The thing that would be absolutely wonderful to have researched is whether the people who are offered anti-depressants instead of levo, when their TSH is elevated but 'in range' a)actually are depressed when evaluated via the standard tools like the Edinburgh test and b)get any better when they take the anti-depressants.
We all know in our hearts what such research will reveal, but its always a good idea to have evidence! The tricky part will be to get a suitable cohort. You would probably need to find a few co-operative GPs who allow you to interview the said patients at the beginning and after a suitable period of treatment. The few that find their way onto this board aren't really that representative. Mind you, GPs might be really happy to redirect what must be heartsink patients to them.
Even better would be to do a controlled trial comparing levo, antidepressants and no treatment. But that might be difficult to get approved and done in a psychology setting because it becomes 'medical', and there would be funding involved.
Or you could look at depression symptoms in patients (on levo, probably because introducing such concepts as T3 or NDT would probably be a step too far) and see how they correlate with the Ts. TSH is a blunt instrument but probably adequate in such a case. You'd need a control group, but there are plenty of almost sane people in universities!
If you could show that higher TSH (say over 2.5) correlates (or doesn't) with more depression symptoms that would be of value too. And that could be conducted via members here. All you have to do is ask those who are on levo to fill in a questionnaire, and give you their latest test results. You would need a larger sample than 100, but it should be reasonably easy to come by - and I imagine that Louise would give you her blessing and let you send out a blanket request for participants. You could do the whole thing via one of the online survey tools, so that data handling wasn't too onerous. (the likelihood is that the uni already has a subscription to one of those services)