So, been going through your song list. I am not comparing to a leaner headphone in the bass. Just trying the tracks out. The bass on these is definitely very present. It sounds like the BGGAR target is a bit too much bass for you. I personally love it and find this list shows off what the timeless can do.
FYI, bass reducer eq on Qudelix cleans this right up. And I can completely understand where you are coming from, the bass moves to the background instead of being the feature of the songs.
What ifi product are you on?
FYI: Dunu Zen may be a ridiculously good target for you. Takes down the bass sonics a bit while kicking up the slam and texture. Lean and clean. It does roll off the upper treble.