Stop focusing on building your brand and start focusing on distributing your product. You need to accept the fact that for whatever reason, people choose to label you as a foreigner because you cook ethnic food, so you lose branding credibility. Therefore, you need to outsource your branding. You can leverage your distribution channels to increase distribution and build your brand simultaneously. Your distribution channels are a) your restaurant, and b) a catering business. Why not sell your food to other catering companies? There is no reason for it to be exclusive to your own. When more catering companies sell your food, you control more distribution channels and move more product. Your product is your food, and that is what differentiates you.
Reduce the cost of preparing your food [1] and outsource distribution. Allow catering businesses to serve your food. Tell them you will give them a discount if they call it "<Your Last Name> Food." [2] From the sounds of it, customers love your food (demand is high) and few people know how to cook it (supply is low). So price can be high. Just show catering companies how much they can charge for your food, and they will jump at the opportunity to buy your food at seems like a large discount. Not only will they distribute your food, but they will build your brand because a positive brand for your food increases their sales.
[1] Start by reducing cost of labor (chefs, sous chefs, dishwashers, waitstaff) and inventory (make more efficient shopping trips).
[2] The name of your food is your only branding decision. Choose a good one.