Here is a link I found for you.
Well you might try getting seeds of other Hymenocallis species, and seeing if any do better, or just keep it simple and grow out lots every year, keeping the best, like the Knock-Out Rose guy.
I have an Intermediate Bearded Iris that does well called 'Midsummer Night's Dream' (unlike all the fancy cultivars of TBI I bought. It reblooms every late-summer and fall, is blooming now. Here is a photoof it last October 18. Also the white rebloomer 'Immortality'. Also I have been messing around a little with the little Irises, really just getting seeds to start of oddballs. Have not yet intentionally bred any,maybe when I retire...
http://www.aces.uiuc.edu/vista...