Every year or two I give drop bars another try... then stop. Most recently I converted my single speed commuter from dirt drops to swept flat bars (Salsa Cowchipper to Salsa Bend). They have a moderate sweep, not like a Jones bar but more like a MTB bar for people who never stand on the pedals... and they sweep forward first so they are still nearly as reach-y as a drop bar. Clearly this isn't the right look for whatever had a mustache bar, but I'm sure you could find something similar in the VO / Soma / Sim Werks vein.
whatbars.com