Thee, thou, and thy held on among Quakers in the Philadelphia (USA) area, at least 30 years ago. The older Quakers used it often among themselves; younger ones rarely used it but could produce it correctly when needed.
It was still used in Sheffield in the 50s and 60s, although more usually as an emphasis when having a go at someone 
Much better be known as the one who smiles without provocation, than the one that “tutoies” everyone 
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Thou is still used, live, in Yorkshire. As thou or tha’
Oh dear, Vero, now I am going to have this vision of any adult that goes around tutoie-ing everybody, as a giant adult-sized baby in a big nappy.
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I was talking gently with a man whose Mum had just died… she was with us, in the room.
As he and I talked back and forth… I slipped and started using “tu”…
As soon as I realized what I was doing… I apologised.
He thanked me for being so kind and explained that I had said just the right things, in just the right way… no apology necessary… phew.
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I agrée, on my experience “amicalement” is used where business contacts have become more than that, and would be considered friends. It’s definitely not luke warm.
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Well it depends where you are coming from! If it is a progression from cordialement, then fine. But if it is someone who has put you up and hosted you in their house and with whom you have got on extremely well (which was the original question) then I would view it as distinctly lukewarm!
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Yes I agree in that case!
strikes me that we’ve all given a wide range of possible endings…
Over the years… I have probably used more or less every single suggestion folk have made…
if folk wish to dispute the use of amicalement… fair enough.
I’m quite happy on the occasions folk have used it to me… and to whom I have offered it…
for me the content of the email is more important… 
I love it!
It’s best not to show all your teeth !
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Luckily, I have beautiful teeth. (Born in Montreal, where they first fluorinated the water). Though, the rest of me is falling to bits 
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Just thought I’d add to this thread with an email we just received, ending with four, count 'em, four closings:
Je vous souhaite le meilleur.
Au plaisir de vous revoir très bientôt.
On vous embrasse.
Bien amicalement.
It made us feel all warm and fuzzy.
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