I love hesperaloe too--it's one of my very favorite plants. They can be divided most times of the year, but the *best* time in my opinion is early spring when they won't have to face coolish wet weather with open cuts. I usually try to divide mine in March or April, but I've done it virtually at all times of the years (you know how impatient gardeners can be!) and have had great luck.

I would just try to avoid the two extremes of the year: mid summer and mid winter.

I just use a shovel and dig them up with plenty of roots, shake off soil if necessary and lay the clump on its side and then slice through the roots to make new, large divisions. I let them air-dry in shade for a day before replanting. For some massive clumps, I've been known to just cut out a big division and then backfill with soil (after letting the main clump and new clump air-dry for a day). They aren't too fussy and they want to take over the world, so they'll be fine as long as you give each division plenty of roots.

Good luck and keep us posted!
Take care,
Grant

Oh, I forgot to mention, that a lot of times the outer leaves will flop over when a division is re-planted. It's usually not technically wilting from water stress, but more of a flopping from not having nearby crowded leaves helping hold nearby leaves up.

I have a huge clump out front I really should divide. Guilt guilt guilt, LOL.

Good luck again!
Grant

The important part is letting the cuts air-dry for a day or two, in the shade, before replanting.

Also, replant them in a dry hole, and wait a couple weeks to water them.