I didn't answer this part. I believe we danced all through night at Arty Farty and it was like 7 o'clock when we got kicked out. GB is usually open til 3 or so. Kusuo which I think you should should visit as this is a touristy Japanesey bar. It's fun and people there are nice usually (LHR/MEL/Europe FF would agree. hehe). And they are open til 5 or so.

I am usually good at suggesting places (including non-gay ones). Should you need something like this, you can let me know. I'd be delighted to gather some places you should visit in Tokyo (BTW, the homo district is not strictly limited to Shinjuku. There are other homo districts and they can be fun and different as well

Happy travels!