Obviously we can't go on with me deleting the chart and the author reinstating it, so I have asked WP's conflict resolution people to look into it. Meanwhile I would be glad of any comments about the disputed chart and whether the phonetic values in it look correct.
For those not familiar with Wikipedia, each article has a "Talk" page associated with it where you can read the discussion about controversial matters in an article - the discussion about this vowel chart is in the last two items. (I find it hard to get to the Talk page of an article when I am using the iPad version of WP).