Hi Jack,
You nipped in between my two posts  ::)
With respect, your post covers a lot of situations (including whether you should apply for residency here).
I think the health cover issue can be split into two main sets of circumstances i.e.
1.  Your main residence is UK and you come here for varying length visits.
2.  Your main residence is here and you may well visit other European countries (including UK).
I'll try and pin down the sp for both.