Unfortunately we can't reschedule the trip but we might move our summit bid up from this Thursday to this Wednesday based on the current weather forecast. With all the snow this past weekend, would snowshoes be useful on the Mountaineer's Route, up to UBSL or Iceberg Lake? Or are snowshoes likely to be more trouble than they are worth on most of the Mountaineer's Route trail?
Snowshoes don't work that well on angled surfaces. That's why it's hard when the snow hasn't consolidated. Have you ever checked out windy.com? I love it - click on the cloud overlay option and zoom out a bit. You can see the entire Pacific storm track is aiming right for California:
So, as you've probably already checked, NOAA is saying tomorrow and early Wed is your best window. Thereafter, it's going to snow.
Honestly, and you probably don't want to hear this, but you might start thinking of alternatives. If you're going to be in the E Sierra anyways, then Mammoth is a good option for skiing or snowshoeing. Even though it will be snowing there as well, you could stay lower down near civilization to be safe:https://forecast.weather.gov/MapClick.php?lat=37.6488&lon=-118.9779#.XNm9TY5KiM8
The other option is White mountain. No matter how you slice it, your trip is going to coincide with another winter (spring) storm warning.