Landlord told us to move units or leave after we complained about garage door noise disrupting sleep. Are they liable?

Location: Rutherford, NJ

We live in an apartment directly above the building's parking garage exit. The garage door operates starting as early as 4:30am, and since it's the primary exit, it cycles repeatedly throughout the morning as people leave for work. The noise transmits as vibration through the building structure into our unit, it's not just sound, it's felt. We've measured it above 44 dBA (57dBc), and the low-frequency character makes it more disruptive than that number sounds.

We raised this with management a few months ago. A technician looked at it and said the door was mechanically fine, so nothing was done. We recently followed up in writing, explaining that the issue isn't whether the door works but whether the installation uses vibration isolators to prevent transmission into the units above. Pretty reasonable ask.

We then spoke to them in person and they told us flat out: they're not going to fix it. Our options are to switch to a different unit in the building (at our expense) or move out.

So my question is: by refusing to address what seems like a habitability issue and instead telling us to take on the cost of moving, are they exposing themselves to any legal liability? Constructive eviction? Breach of implied warranty of habitability? Anything else worth knowing?