Interestingly, along those same lines, Mary’s House in Ephesus attracts as many if not more Muslims than Christians. Interesting article about the site is here: http://www.aboutkusadasi.com/ephesus/virgin-mary-house.html (of course, the fact that it’s in Turkey wouldn’t have anything to do with those statistics)
Self-ping for that article later. I visited the house when I was 17 and, although not particularly religious at the time, was swept away by the whole Ephesus thing.
My wife, a Catholic from India, does tend to affirm the stories that tell of Muslims venerating Miriam.