Editions rarely have any Platinum recognition. If that's important for you I'd go for the Meridien. If it's not, I find it hard to imagine the Edition will be better than the Hotel Arts (but as I've not yet tried it - I could be proven wrong here).

The Meridien should absolutely allow SNAs and is usually very generous to Platinums in general. Try calling Marriott (haha) to get one submitted.

Cotton House looks gorgeous, but I've never stayed there, so any comments above shouldn't be read as an implicit criticism of the venue. Marriott really has a sweet spot in Barcelona - one of the best cities in Europe for options.