Update 1: After just 10 minutes, the electrolyte has turned opaque black and the current is up over 6 amperes. Should I dilute the electrolyte more?
It depends on how slowly you intended the experiment to progress. Typically, once I start adding HCl, eventually the deposition process accelerates rapidly, and current increases to around 8-10A (at 12V) unless the electrodes are in a short-circuiting state. At this point the resonating sound would start, presumably generated by micro-explosions in the gap portion above the electrolyte level.
Interesting that with the mild steel electrodes the process seems much faster than last time. It makes sense if the other ones were made of stainless steel, though. That also probably means that with SS you could use a narrower gap than what I observed to be manageable with no direct width control means.