Thanks for the replies which came up so far.
My short answers:
No film defect, as it occurs in two sorts of film.
No dimpled bottom of the tray either, as only the backside of the film touches the bottom.
The gloves are powdered inside (I think), but not outside.
The patches also don't appear to be prints of naked fingers, as the pattern is different.
And yes, they also appear to me like the prints of a gloved hand; but what could them make to appear? The latex of the gloves?
I might text with distilled and non-distilled water, but I was hoping to find somebody who saw this before and might be able to give some advice before I start wasting my sheet films (though when I continue to develop my precious negs as I did, I am afraid I am also wasting them).