Holy shit, that worked! I just happened to have an HDMI dummy plug that I purchased for my RX 570 rig but didn't end up needing. I plugged it into the first RX 560 on the Onda rig and now the correct clock rates are showing up in GPU-Z while Cryptonight hashrate jumped by ~22 H/s per card (after stopping and restarting xmr-stak)! I'll try Claymore v11.0 on a <2GB DAG Ethash coin (MUSIC or UBQ) in about 15 minutes and update this post.

I have just one merit left to give out, but if solving a problem I didn't even know I have isn't worth a merit then this forum is screwed...

UPDATE - okay, looks like I need to get a dummy plug for *each* card; the hashrate jump in xmr-stak was ~66 H/s total and I *assumed* that it was spread equally per card, but when I loaded up Claymore only the first card shows a higher hashrate of 14 MH/s while the other two are still at 12.9 MH/s. Still, the dummy plugs are cheap and an easy fix!