High pass, shelf, and peak are all filters, just different shapes.
I generally prefer minimum-phase parametric filters (standard parametric EQ) to fine tune the curve for correcting low frequency problems by ear. High-pass/low-cut (same thing) filters are way too blunt an instrument for me.
But with extreme bass and the DPA omnis which have flat sensitivity to way down low and soak it all up, I've found things can get weird with the necessary EQ corrections required to clean up the recordings for normal playback. I've not analyzed that deeply as I don't record in those situations very frequently, but I suspect the issue may be the large phase shifts introduced by minimum-phase filters making such high magnitude corrections.
I suspect a linear-phase EQ filter may work better. Indeed FFT filters are linear phase as I understand it.
Manipulation of the dynamics may also help. But I suspect EQ will be your first line of attack. Multi-band compression is essentially dynamic EQ, with each band roughly corresponding to a wide graphic EQ channel.