Spikes or Spikeless

With a little finessing and tweaking of the spikes, it should be very stable through the carpet and into the concrete.
You need spikes that are long and tapered sharply to get through all that padding. I made some platformes for my speakers with adjustable spikes because I have carpet on top of wooden floors. The platforms gave it some mass to clean up the lower end. But with concrete floors, that should be plenty of mass.
If it takes to much of the fullness out of the bass, just inch it closer to the wall to help fill it out.
Take small steps so you don't get to much bloom in the bass. It's a PITA, but when you nail it, all will be good.

I have had good luck with spikes over concrete,with an area rug under the speakers and 1" thick Maple between rug and spikes..Spikes grip into Maple and are stable with the weight of the speakers holding everything down..The Maples is just cut 1" thick, 2"x 2" square under each spike.....