I don't have a specific brand to recommend, but metal dishes of varying sizes (from small condiment plates to very large soup bowls) are used commonly in Korean dining. You can also find double walled stainless bowls which insulate well to preserve the temp of your food and hands.

If you ever replace them it may be worth getting machine washable rugs. They're not bifl, but sometimes I think it's worth it to compromise on longevity in favor of cleanliness and low-cost/effort maintenance. A small, low/no pile machine washable rug is easier to find durably constructed without quick-to-fail rubber backings than larger area rugs are.