I think this topic is different than the one @Jazzbass19 linked. Here it’s about the headphones directly plugged into the amp and the other one was more about the recorded sound of the bass despite the title.
I always used my Sennheiser HD 580 Precision. They are not low heavy or boomy at all so I usually thought they were not very bass heavy but it seems they are precise in the low frequencies as you say. I’d expect them to be costing 300DM back in the day.
If I didn’t have any and would buy new ones I probably would take a look at the Beyerdynamic DT Series. I can’t remember the number of the model right now but I’ve heard it recommended as often as the rumble amp is recommended here.
I could also try using the cheap in ear ones I use for travelling once I’m back at home. Just to have a contrast to tell if it’s as bad for me too with low quality headphones.