The phrase "never even" in spoken English - Bookish ? Old-fashioned ? Sophisticated?
Solution 1:
In the Norfolk dialect 'never' has a wider range of uses than in standard English.
This is from the Wki entry on the dialect, written by myself.
'The word 'never' has wider use in Norfolk dialect than in standard English where it only means 'not ever'. Norfolk people will frequently use never simply as a way of saying 'did not' as in 'he never went'meaning 'he did not go'. It is also used in Norfolk as an interjection. Someone who is suddenly shocked by some remarkable fact they have just heard may say abruptly 'Never!'. e.g. Person A says:'They are expecting their fourteenth child'; Person B says 'Never!'
It is the case with many idioms that Norfolk retains older speech forms that were once prevalent in wider English. Clearly 'never even' is such an older form.
Solution 2:
It took me a while to try to work out an objective way of answering your question. Here's my attempt:
A google search, limited to the UK, for the phrase "never even", returned 'About 7,620,000 results'. Reading levels of these were: Basic 82%, Intermediate 17% and Advanced 2%.
"Didn't even", returned 'About 303,000,000 results' at reading levels of 73%, 26%, <1% respectively.
For the US, "never even" returned 'About 42,600,000 results' at 70%, 28%, 2%; "didn't even" returned 'About 3,200,000,000 results' at 67%, 33%, <1%.
You'd have to run some statistical analysis on these numbers and take a look at the kinds of writing the phrases appear in to get a picture of the way in which they're used, what TV or radio programmes they're linked to, which will give you an idea of demographics in terms of the target audience which is being aimed at, and determine how much to take this into account.
On a subjective level, I'd say there are subtle class signals in BrE associated with 'didn't even' that are less present with 'never even', but you'd have to do a sampling of other users to see how widespread this impression is.
For an example of 'didn't even' in relation to social standing or practices in AmE see this NY Times article, in AusE this Telegraph article, and BrE in this Independent subheading.