Again, Yamato English website does not list the service, but on Yamato Japanese website list Yamato Courier service which handles items too large or heavy for Yamato TA-Q-BIN service. Also, JAL ABC service (delivery service to/from airports) also list over size item delivery service such as surfboard. Again JAL ABC website mention oversize item delivery service only on Japanese website, not on English website.
Delivery service counter is located at arrival level floor on the airport terminal. Upon arrival at HND walk over to their counter and show your surfboard and ask about delivery to Narita Airport. Beside the cost and need to pay additional if you want insurance, large item delivery service cannot specify delivery date and time like TA-Q-BIN. However, OP said spending few days at Tokyo so hope sending surfboard from HND to NRT will not be a problem, time wise.