I'm sure many people have figured this out before me but the key to properly enjoying the HPA4 is simple -- get a DAC that can do +24 dBu out. Benchmark even says this in the manual, to quote: "Tip: We recommend using professional-grade balanced XLR interconnects that provide +24 dBu at 0 dBFS. Consumer-grade balanced XLR interconnects operate at levels that are about 10 dB lower (4 Vrms or +14.2 dBu at 0 dBFS)." I did read that upon purchase but didn't fully understand the implications at the time.
Specifically, the HPA4 is unity gain at 0 dB on the volume control, with only +15 dB of additional gain available on top of that. In other words, a consumer-grade DAC with an XLR connection to the HPA4 can at most result in 4v from the headphone jacks with volume at 0 dB. This is no problem for the vast majority of headphones, but it leaves the Abyss with little headroom if you're playing a quietly recorded track or have some DSP in the chain like crossfeed or bass-boost. And apparently the Susvara (which I don't own) hurts even more.
The solution? Get a DAC that can do proper +24 dBu out, like the RME ADI-2 Pro (which I now have) or one of the Benchmark DACs. This limits your choices of course; you'll need to shift focus away from boutique consumer manufacturers to those more in the pro audio space, but if you're of a more objectivist bent like me then that should cause no worries. Now your volume control is rocking out 10 dB lower and you have plenty more space. This doesn't get you any more power (watts/current) of course... it simply allows you better ACCESS to that power. Certainly it's got the Abyss TC fully covered. The insane Susvara might still be able to pull more power than the HPA4 can provide, but I'll leave that to others to experiment; as someone who's not a fan of HiFiMAN's house sound I'm never going to own one.