There would be times when you could use during as a sub for while. Ex While I'm at my appointment you can read. Or You can read during my appointment.
I have my thesaurus bookmarked. It's a great one because with one click, I can switch to the dictionary. Here is the link: http://m.dictionary.com/t/?q=while&subm ... CHT=Search
It does have whilst as a synonym. The three definitions are as long as, even though, (conjunctions) and time interval as a noun. It also has synonym s for each definition.
And I think the UK spellings lean to whilst, they also tend to use other words that end with t like dreamt instead of dream. Some people not familiar with the UK spellings will think things like colour and behaviour are typos, but I think it's good to not "Americanize" your writing, unless you are writing exclusively to a US audience. It's good to broaden one's horizons.
Oh and personally I think whilst sounds more romantic.