I don't know why I can't pee in earshot of men but I just can't! It's not something I have concious control of. I personally wouldn't have a problem with the tampon dispenser but I know some women would. It is different from buying in a shop as you don't immediately go and use them in a shop with the sounds of unwrapping etc. Don't forget not all men are above making sexist comments in the street- some will undoubtably comment on a womans cycle if they know it. 'He's out of luck this week she's on' is a comment I've heard directed at women. Do you really want to share a public toilet with 'white van man' and his mates?
I have no wish for public unisex toilets for the simple reason that the men's always stink. Yes you sometimes get splashes on the women's seats, but I can't imagine what you'd find in the men's, judging by the smell!
As for queues at the women's - surely that's simple. It's a well-known problem and so there should be more space allocated to the women's toilets than the men's, maybe 2/3 to 1/3.