Seasonal jobs that might turn permanent (Omaha)

A retailer and two warehouses near Omaha are hiring seasonal staff. I have read a lot of threads here and could not find my exact situation. I would like to avoid a gap in my résumé. Is it worth applying to several at once?

Apply to several. Start dates and schedules change quickly and having options helps.

Keep a list of supervisors' names. A reference from one of them helped me land my next job.