Right, this is a complicated area as I'm sure you're aware. As far as I know (and I am not a lawyer):
I assume you've tried to be counted as a dependent on her student visa. This won't fly - to be considered dependent in the UK you generally need to be related by blood (eg parents/kids). I don't think you can be considered as a partner either if you're not married.
You are allowed to be in the country for 6 months as a general visitor and don't require a visa for this (you'll get a form on the plane to fill in, see
http://www.ukba.homeoffice.gov.uk/vi.../requirements/). After that you have to go - end of. You can't extend the visa past 6 months and you can't change to a different category of immigration.
There's no specific guidance in the rules for US nationals (due to visa exclusion you're handled differently) but the general Visitor Visa advice reads as follows:
Quote:
There is no restriction on the number of visits a person may make to the UK nor any requirement that a specified time must elapse between successive visits, The fact that a person has made a series of visits with only brief intervals between them would not, in absence of any other relevant factors, constitute sufficient grounds for refusal.
It is reasonable, however, for the ECO to consider the stated purpose of the visit in the light of the length of time that has elapsed since previous visits. A visitor should not, for example, normally spend more that 6 out of any 12 months in the UK (but see guidance relating to visitors for private medical treatment).
So basically I think you can visit for 6 months, leave for 6 months then come back.
Regarding getting your name on a lease this shouldn't be too hard to achieve - I'm a national but I've never had to prove that to a letting agency/private landlord. Seems pretty daft that this is how Stars proves residency but hey, it's their show and they can screw it up if they like.
Hope this helps and remember that it's just my interpretation of the rules - the Border Agency are absolute bastards and will change their minds and screw you about willy nilly.