What yield can black rice (chak-hao) give and how do I improve it without losing the type?

Traditional black rice is honestly lower yielding than modern paddy, often well below high yielding white varieties, because the landraces are tall, photoperiod sensitive and not bred for high yield, and that lower yield is the trade off for the specialty premium. You can improve yield with better agronomy, such as proper nursery and transplanting, balanced nutrition with controlled nitrogen to avoid lodging in tall types, good water and weed management and timely transplanting, without changing the variety. Some universities have developed improved or semi dwarf pigmented lines that yield better while keeping the black colour, so ask your state university or ICAR whether a better black rice line is available for your area. Just remember that if a specialty buyer wants the authentic traditional type, switching variety to chase yield may lose you the premium. Balance yield against what your buyer actually pays for.