welcome to hot dogging Whalehead. I think your idea is good. t-shirts are cheap and people like free. i use a couple of promotions that work pretty well.
in winter i offer folks their lunch for free if they can kick an air potato across the pavement and land it in a certain spot. i usually gather some projectiles in the morning. nearly everyone enjoys trying it and about 3-4 people have ever done it. one guy said it was his weekly exercise!
also, about every 5-6 weeks i print up a handful of “Buy 1 Combo Get 1 Free” coupons to hand out. I tell them outright I hope they will bring a new friend to lunch with it, but they can use it however. it works well to bring in new customers.
even with the finest product offering, customers can fade away for whatever reasons and need to be re-encouraged and replaced.
my customers know that when they see the giant yellow bird out, chili is FREE. the bird often calls people in as they drive by. it’s the same as a sign, but more fun.
promotions work for me.