What a great story! It's really beautiful, poignant and funny all at the same time. I love the background you've created for Doge and Dumbledore (a much nicer scenario than the supposedly canon one) and the reason for the wanking in the first place (lets hear it for sex-related magic!)
I also love the fact that you've made mention of homophobia in the Wizarding World, something I haven't seen much of in HP fanfics. In light of Rita's innuendos in DH, it's very fitting.