I believe I can provide some insight on this subject but first, let me list every headphone I've owned with highly rated bass:
- ZMF Blackwood
- ZMF Ori
- LFF Code-6 (modified HiFiMan HE-6, tried with various pads)
- Audeze LCD-4
- Stax SR-007A
- Stax SR-009
I have also listened to many other high end headphones such as the rest of the Audeze LCD lineup (fazors only), HiFiMan HE1000, Abyss AB-1266, Sennheiser HD 800 and HD 800 S, Focal Utopia, Beyerdynamic T1, etc.
The first thing I will say is, immediately rule out all dynamic driver headphones. They don't hold a candle in bass to planar magnetic or high end Stax.
I will just say it right now; the Stax SR-009 has by far the best headphone bass I have ever heard. While elite planar magnetic headphones have an extra around 10 Hz of bass extension (they can extend down close to 10 Hz while the SR-009 extends down to 20 Hz), music hardly ever reaches this low.
While the SR-009 bass doesn't slam the hardest, it slams harder than most, even more than most planars (more than any HE-6, more than the HE1000, thus I would say more than any HiFiMan). Loads of slam making it tons of fun.
The SR-009 also seems to have less general mid bass presence than the Audeze LCD lineup. So why do I rank it #1? Because the bass region, and every other region, is so incredibly transparent and detailed that it unlocks an entirely new dimension of bass compared to any headphone other than the SR-009S which is completely out of budget. It reveals so many more sounds and nuances previously unheard and the differences are NOT subtle.
However, while it can easily be obtained used for well under $3k, it needs at least a KGSSHV amp I would say to best the bass performance of great planars. And a KGSSHV will cost over $2k.
So if this is unacceptable, forget Stax and go with a planar magnetic headphone.
So other than Stax, the LCD-3 has the best bass in your price range but I cannot recommend it due to its unnatural sounding vocals and most instruments, caused by very harmful upper mid and lower treble recession.
So barring Audeze, my recommendations fall to either the ZMF Ori or a HiFiMan HE1000/HE1000 V2. I haven't listened to the HE1000 in a while but the bass extends as deep as possible and is very detailed, but doesn't slam very hard. Whereas the ZMF Ori slams harder than almost all, even more than Audeze, yet it doesn't sacrifice mids nor quality. Of couse the HE1000 is more open sounding, more transparent, detailed, etc.
Summary = Top tier Stax is my favorite if you can afford it, otherwise I suggest either the HE1000 (if you want super deep, detailed bass and will sacrifice bass slam for wide open, detailed, airy sound) or ZMF Ori (tons of slam/impact with top tier extension and breathtaking quality but in closed back form factor, sounds more open than most closed backs though).