Update: I finally received the new case, backplane and AT power with it. And surprise surprise, it solved most of my issues 😀 Now aweutil runs, my Audician 32+ can be initialized (prior to this, it wouldn't work at all) and even USB on the SBC is working. Great success!

However, one problem remains: Duke3D with my AWE64 plays only one channel of audio. Other one is silent.