I don't think I'd do the 'purple robe' thing. That's just a little over the top.

However, getting one of those nifty purple and gold sashes that you wear around your neck, the one with the outline of a dead fish and a loaf of bread... looks pretty official. It's easy to put on quickly, no matter what you're wearing, and you can keep it in your glove compartment for when need arises. Wearing a sash immediately distinguishes you, because 99% of the public doesn't wear sashes.

A brass or copper religious ring, or a bracelet, with a cross on it is always nice. It completes the outfit.. and you can create an entirely B.S. story about where you got it or how it "came to you" it if you want that will more than convince the normies.
I like keeping it small and non-dramatic. It puts people at ease. The more little visual cues you give them, the more they feel like approaching and asking questions. It's best in my opinion to be approachable and non-threatening.

Even police and EMS and hospital workers are used to giving some accommodations to "clergy" that they would never give to the general public. Bells & whistles interfere with that. Simply showing up with a lanyard or sash, a little cheap religious jewelry, a sincere calm attitude and a credential badge may go a LOT further than you'd think.