South slopes as seen from town are almost completely bare below 11,000'. I haven't seen other aspects of the peaks since I was last up there on the 15th. If taking the Dutchman route I describe, and given the melting we have had, I would say that you can use the snowshoes if you want to, but can probably get away without using them. Crampons or just boots going up are probably sufficient and you might just use boots all the way down. We haven't had snow in 5 or 6 weeks, so the season is pretty much over. Unless we get a welcomed freak snow in the next few weeks, its going to be dry to monsoon season and the snow will continue to deteriorate. That will mean a mixed bag in general, but with a dense surface corn layer that will require nothing more than a water resistant boot.
Technically the permit is required until April 15, but at this point I would skip it. Your call.
I think Monsoon season will begin around June 20, plus or minus 5 days, not by the calendar according to the NWS, but when dew points rise dramatically, and it begins to rain over the Sacramento Mountains. It will start about 10 days later in Arizona.