I don't see rugs/carpets being very effective, they would be more effective at soaking up the higher frequencies. Whereas bass is no respecter of walls and floors, regardless of room treatment. The only effective remedy for that would be an added layer to what you have, with an insulated cavity. Effectively a 'room within a room', but obviously out of the question in a rented property.
Decoupling the speakers from the floor as much as is possible may be your best solution.
I just dropped in, to see what condition my condition was in
T/T: Inspire Monarch, X200 tonearm, Ortofon Quintet Blue. Phono: Project Tube Box CD: Marantz CD6006 (UK Edition); Amp: Musical Fidelity A5 Integrated.
Speakers: Zu Omen Def, REL T9i subwoofer. Cables: Atlas Equator interconnects, Atlas Hyper 3.0 speaker cables
T'other system:
Echo Dot, Amptastic Mini One,Arcam A75 integrated, Celestion 5's, BK XLS-200 DF
A/V:
LG 55" OLED, Panasonic Blu Ray, Sony a/v amp, MA Radius speakers, REL Storm sub
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