"Your and my [something]" vs "Yours and my..."

Prompted by comments against this question, I'd like some help figuring out why some people (myself included) prefer yours over the apparently more logical/grammatically consistent your in this kind of sentence...

Yours and my native languages have co-existed for hundreds of years.

Google Books has Your:Yours ratios for languages:2:2, parents:9:10, houses:4:2. That's a very small sample size, admittedly - but even without anything like that, I know my own usage. So I'm not really interested in being told which is correct, except insofar as this has a bearing on my question itself - why do some people, (including some "careful speakers", which I don't necessarily claim to be) use the apparently incorrect form?

EDIT: It may be important to note (as @Gnawme guessed without it being explicitly stated in the first version of this question) that I personally would use singular language in the above. It was just too difficult to search Google Books for that particular distinction, so I said nothing about it.

The OED’s definition 3 of yours is ‘Used instead of your before another possessive, etc. qualifying the same noun. Now rare or obsolete.’ An illustrative citation is Joseph Addison’s from 1710, ‘I suppose you know, that I obeyed your's, and the Bishop of Clogher's commands.’ (Note the apostrophe, incidentally.)

As you have said, the written record tells us nothing about what occurs in speech. 'Yours and my . . .’ may occur as frequently as you suggest, but I think we're at least as likely to hear ‘my . . . and yours’ or ‘your . . . and mine’ or ‘our . . .' Or 'your and my . . .' or 'my or your . . .'

If you reverse the persons mentioned in your sentence, then you get:

My native language and yours have co-existed for hundreds of years.

This is a perfectly grammatical sentence. Good manners dictate that we mention ourselves last, hence the more polite form you suggest Yours/Your and my native languages have co-existed for hundreds of years, which could of course be Your native language and mine have co-existed for hundreds of years. The latter raises no problems, either.

If I ever used the construct you prefer, I'd do it unconsciously, and seeing it written, especially by me, would make me want to correct it immediately to the more grammatical Your and my native languages... I suspect the reason I might use it would be because there is no noun following your, which doesn't sound natural, especially when we speak.