If you get to Nirasaki around 8:40 in the morning, the bus (I’ve noticed the link above is broken – the new timetable is here http://www.kyohoku.jp/info_diagram_list.html#info_dig_miz) gets you to Mizugaki-sanso by 10:00, and you need to be back by 16:30 to get the return to the station. So it’s doable at a fairly slick pace; but I’m not sure it would be that much fun, and you wouldn’t have any room for error.

Personally I’d recommend getting up there on a Saturday, climbing Mizugaki, either camping or staying at the hut, then do Kinpu early the next day. Or do what we did, and camp part way up Kinpu and hang out on the rocks in the sun. Kinpu’s got some great views, both on the way and at the top, and it would be a shame to rush by without seeing them because you were pressed for time.

It’s possible there will still be snow till late May, especially on the northern side of Kinpu in the forest that you climb through – there was when we went around this time last year. What you often find is that the snow on the trail to the top gets compacted and icy as people climb through the winter months, which means it lingers late into the season. Crampons (4/6 point should be fine) were necessary last year – we went on the 13th May. There’s been quite a bit of snowfall this year too – on the way back from Yari last weekend I could see the top of Kinpu still had some snow on it. By then end of the month it should be clear.

Wes has a good writeup of the route at his site:
http://japanhike.wordpress.com/2008/04/22/mt-kinpu-%e9%87%91%e5%b3%b0%e5%b1%b1%ef%bc%89/