That's a lovely plant Chris! I have not grown that..but for my other iceplant-like plants here, I do the cutting in Spring after blooming, or in mid Fall as temps are still cool. It is nicer in Spring though, days are getting longer, air still cool, enough time for the cutting to acclimate and grow roots as the soil is warmed up by the sun.
Ice plants in coastal areas in the SF Bay area here, thrive year round, they got the cool ocean breeze cooling them down while basking in the sun. My location is more inland, so once the Spring rains are done, it is dry and drier, warm to hot, puts most of my succulents in somewhat semi-dormant state.