Detergent is not a disinfectant.
Detergent (and even good old soap) doesn't kill _all_ bacteria and spores, but it's pretty efficient in killing most of active bacteria and fungi (link: http://www.ncbi.nlm.nih.gov/pm... ). That's more than enough to delay the onset of mold long enough for the clothes to dry.
Are you really going to get up at 3AM to do laundry? I doubt it.
People on Kauai, HI do this all the time - by setting a timer on a washing machine (electricity prices 8x the national average are a good motivator) . You can also pre-heat water during the nighttime or use solar water heaters during the day.
He has not acquired a fortune; the fortune has acquired him. -- Bion