I use 'mail' countably when referring to email, so I'd happily say 'junk emails/mails'. To avoid this, you could say 'another piece of junk mail' or 'some more junk mail'. In the UK, I have seen no compalints about 'mail' being used countably, but some complaints among American speakers. I see no reason for this- we have posts on the forum and emails in our inbox. Without 'e' or 'junk' it sounds strange to use the plural. I think pragmaticism will win this one.
I think you are right and I don't have any problem with "mails" either. I am sure that the countable mail is here to stay. We could have used "e-letters", but now it is too late and at the end of the day, it doesn't matter. My problem was that in the original sentence we have a "mixed" form: "one of my mails" would be OK by me.