Well, you don’t necessarily need to deal with the laundry the second the machine is ready - if you merely set the alarm to be the approximate maximum time, you’re probably going to be fine with the laundry spending half an hour or so sitting wet in the machine.

If the alarm is easy to dismiss, then perhaps a reminder app could be of use. I frequently use Google Tasks with a time for the tasks to cope with everyday life, which sends a notification at the specified time.