When the leaves fall over they should be ready to dig and dry out, but I wouldn't think you want to dig them while your weather is still hot. The leaves are what puts the energy back into the corms. They probably will stand the move IF you take care.

Ditto on what Wally said. Glads are like Dafs, Tulips etc. The leaves feed the corms. Here's my take on it. Caveat however: This is simply from experience in my zone 7 garden where Glads for the most part are perennial, others mileage may vary. The corms that will bloom next year are ones formed this year as offsets of the original corm (which withers away after blooming). If you dig them in the fall and store them you will have the problem of maintaining the right conditions for them until next spring. If you leave them in the ground and they over winter for you, then you can simply dig them up when they first show a hint of green in the spring and transplant them to the area you desire. Hope this helps.

I need to move my glads this month, 'cause my neighbors are putting up a fence in preparation for the arrival of their first child, and once the fence is up, I won't be able to get at the glads. If I can't wait for the leaves to die back, any advice about how to move them without killing them?

If you have to move them, and you have soil with enough clay to hold it together, you should be able to move them with enough of the soil that they will continue the regular seasonal decline. Al