I agree with you Lass, although I think perhaps I took it further than I should have when commenting yesterday.
It's hard to find the balance; you spend your whole life telling young women and girls not to be ashamed, not to hide themselves away, that no-one cares as much as they think they do - adults don't care - we're all grown-ups, we all know how bodies work; and you do it knowing you're fluffing the truth a bit (because a lot of people can't help that they care - it's the way we've been conditioned) but you do it so that they might feel just a little bit better about themselves and that things might slowly, slowly change.
So you put aside your socially conditioned urge to hide yourself away, and you do it loud and proud in front of other women; younger women in particular; and it can rile so much when it feels like the hard work you and other feminists have done in setting aside your own discomfort for all this time is being undone by the public protestations of feminists who say "we do care, women do care, we want to be able to hide ourselves away" - and you feel for those poor girls who were starting to feel that confidence and you know it's just going to ebb away....
But of course there is privacy and dignity; there are aspects of periods you should be able to hide behind closed doors, but I don't think those things are using a vending machine, taking your handbag into the cubicle or having sanpro on show. So yes, perhaps I went too far saying we should all push back on everything, because perhaps I'm the type who would push back beyond the line just so the line could settle somewhere a little more moderate for the majority.
So OP, I've been thinking; if this goes ahead and these end up being your loos - and they don't have basins in the cubicles - you could perhaps lobby HR to provide little baskets full of sanpro in each cubicle and a packet of baby wipes for bloodied hand cleaning. If there is not shelf you can get little baskets that sucker to the walls. To be honest, this is the kind of guerrilla action I would take anyway without involving HR, but then insist they keep it up once initiated!
Obviously this doesn't help the whole bloodied clothes thing, but to be honest there might not even be hand driers in the toilets - so there's no guarantee you'd be able to do this anyway.
Obviously not a perfect solution, but it might help you and other women in your work situation, if these planned toilets do indeed come to pass.