IMO, the time to cut the dam is BEFORE the drought comes. The sediments at the bottom of the pond can stay mucky for a long time!
Do you have a low spot downstream such that you can set up a siphon now to drain the pond?
Once I committed to breaching the dam (sorry, that sucks), I would pull down the pond and cut through the dam ASAP. Then your material can start drying. If you get a hot, dry spell in the forecast for late July - early August, then you might be able to get all of your dam/pond rebuild work done in that window and your dirt movers do not have to fight rainwater trying to re-fill your pond during construction. (That always adds time and costs.)
(If your current pond bottom has some loose sediment on top of the firm bottom, there is also a point where it is mostly dry where it would be most effective to push that material through your dam breech and recover your full pond depth.)
Just throwing out some thoughts for you to consider, since you have actual eyeballs on the problem, I am sure you can improve on that.
