I have considered it and in a way I am. I have a bit of an Alexander name like you put, only more like Alexandra...
I simply leave off the 'andra'.. My boss calls me 'Alex', I sign as 'Alex', I order things to 'Alex'.. People generally don't even know me as 'Alexandra'..
Still, that leaves out official documents and the like, but it's not like my gender marker on those is ever going to change to N... So, although I have considered it, it seems unnecessary as in: missing the point. I do, however cling onto my androgynous name in unofficial channels - my resume will always say 'Alex'.