I agree, I'd talk the grade skip over with the Principal and teachers who seem very accomodating anyways (wish all were like yours!). It seems she's doing the majority at Grade 4 level anyways. As Grinity asked though, is it regular 4th grade or are they including her in their GT that starts at 4th? Would it cause her to have to change to new classes for 4th with the GT program if she were to just move up?
My DS8 is in 4th (skipped 2nd) and his organization skills are scattered at times but he gets by with little reminders from me, and the attempt to get him into patterns with homework, writing things in his journal, etc...At this level they still have time to work on those skills!
As for the DYS application, I say why not, its worth a shot. Do you have portfolio stuff that you could include? That way when you send in the Broad Math score over 145, and the just about there WISC score they have a little more of a picture with the portfolio.