I should add that concrete slabs and the like are not an option.
Would you rule out wall-mounted bass traps?
Perhaps my experiences of how room structure effect the sound is not typical but I have found that suspended wooden floors in old properties with thick soft-ish brick walls and lime & plaster mortar really damp the bass well so that there is negligible bass overhang. Subjectively, bass just doesn't appear to linger after the note has ended in these type of rooms.
On the other hand, concrete floors (incl. wood over concrete) with concrete ceilings and concrete block walls usually exhibit harder- hitting bass that hangs around after the event ('thunderous' would be a good way to describe it).
What I'm saying is that no matter how you support the speakers, the room structure may have a bigger influence. You could try strategically placed (and possibly disguised?) bass traps - it's likely to make some difference. And, as you mention, rugs might help too. But before you go down the room treatment route (if you do) it's best to determine the exact nature of the problem by reading up on the subject and, ideally, carrying out acoustic measurements.
The use of speaker stand spikes is always contentious and you see so many contradictory articles/reviews as to their mode of operation. IMO, spikes couple a stand to the floor - they don't decouple. Whilst the point of contact 'tween stand spike and floor is of minimal area, the pressure exerted is enormous and thus keeps the two surfaces in contact under 'normal' listening conditions. Assuming a 15kg stand + speaker weight, the pressure at the point of spike contact with floor will be >2000 bar so those surfaces aren't going to part company. The use of compliant gunk, like Bluetack, to seat speaker on stand is common and will, to some extent, decouple speaker from stand - though depending on the amount used, may not be very relevant.
You may have conflicting requirements here. Reducing the propagation of bass through the floor (so as not to annoy others in the household or your neighbours) may require a different solution to improving bass quality in the listening room. Good luck with this because there is rarely a 'one size fits all' solution to these problems.