Yakushima to Miyako-jima

What's the fastest way between Yakushima and Miyako-jima? Both seem to be reached from different gateways (Kagoshima for Yakushima and Okinawa Naha for Miyako-jima). Is there any fast way between both?

No best way,
but from this MAR 2018, "Maru A ferry" up route from Naha(Okinawa) to Kagoshima goes to Yakushima
if two or more passengers booked 4 days in advance. (No opposite down route for Naha)
If not, won't be stopping, goes to Kagoshima directly from last port "Naze" in AmamiOshima.
http://www.aline-ferry.com/news.html
(Use Google trasnlate, 2018年3月14日, 2018年2月1日 and 2017年12月12日 announcement are so.)
http://www.aline-ferry.com/kagoshima/route.html
Ferry name "Ferry Naminoue(フェリー波之上)" is so.

So, Miyako-jima first plan may better.