Woody, The Peabody does flood fast, it also recedes fairly quickly also. The River might be a bit higher than say mid July. Poles and gaiters will probably be very useful with all the wet weather of late. But the forecast looks a little better this weekend than it has been in a while. Not having been in there it is hard to say if you will need a ice axe and crampons. If it is sunny out whatever snow there is on the headwall will become soft very fast this time of year making for a whole lot of post holing. I think a lot of it can be avoided, as the head wall is mostly large boulders and rocks. If the Trail is hard to find on the head wall you want to aim for the south east and a obvious “gully “ that leads onto the NE shoulder of Washington. You will exit the headwall not far from the Cog tracks. Have fun.
Opps forgot to metion that the Sphinx Trail might have alot of snow on it above 4,000 ft and corssing the stream on it can be dangerous if ther is alot of water.