[Dear Mr B-----,] While I am familiar with the feeling whereof you speak re: addressing someone by their first name prior to a formal introduction, which no doubt is deplored in Debrett, I can't say I've experienced a great deal of discomfort in discarding the convention.
In emails, I use "yours faithfully", "your sincerely", "regards" or "kind regards" depending on the context. I also use "cheers", which I use as a multi-purpose word in spoken coversation anyway. However, at the start of an email, I tend just to use the person's name (surname if we're not acquainted, forename if we are) or "Dear Sir or Madam" if it's to "complaints@????.com" or "service@????.com" (as many of my emails are).
Now I come to look at it, Christine seems such a silly name. It's like the brand name of a sort of mini-Messiah individually wrapped for your comfort and convenience.
Hmm, well showing my old-foginess I start with a "signature" saying who I am, website details etc. (Though this is automatically included) Then I use Dear (name) <comma> Dear Humphrey, Then the text - all properly written out and hopefully correctly spelt and punctuated. And I tail it with Regards, Blob (or whatever soubriquet that person knows me by) ........ What's more, I write SMS texts in much the same way !!!
(Nights) Actually most of my emails are no different from letters except in the greeting if I'm familiar with the person. This means capitals, punctuation and paragraphs. Well, why not? At my age you simply don't give a toss if people think you're bizarre. It's great.
The thing is, I tend to see emails as more closely related to memos than letters. When I receive an email written like a formal letter, it comes across, frankly, as somewhat illiterate.