Route of Water Transport Kupang-Maritaing-Moa on the map of Kupang

There is an irregular ferry from Kupang to Moa over Kalabahi - roughly every two weeks (October 2022). It looks like an ordinary ASDP ferry and departs from the same port (Bolok), but it is operated by a private company (http://www.flobamor.co.id/site/index.php). I did not add schedules as it seems to too often.
Your best guess for finding out is contacting this company (see website) or looking on the FB website (https://www.facebook.com/groups/973014589725106/) where regular updates appear.

On the long distance (night) ferries there is always the choice between VIP (AC, few people) and ekonomi (fan, lots of people) - the price above is for ekonomi, VIP will be more expensive.

Payment was still cash in 2021, but there is a transition ongoing to cashless payment. The cashless payment is complicated: you need to pay online via transfer (indonesian bank only) or via (indonesian) flashcard (BNI, BRI, Mandiri, ...) The latter you can buy and top up in any Indomaret/Alfamart. An alternative option is to go buy the ticket in the nearest Indomaret/Alfamart and you can pay cash there (at a premium of course). With the payment slip you can enter the port where this paper will be changed to a ticket, with which you can board the ferry.