how have you determined that the decay rate is too long? and at what frequencies? what's leading you to this conclusion?
i would recommend you stop and start all over. you can add bass traps and such but if you're not designing (tunning) these to the problem area and with the right bandwidth, then they are of no use or make the problem worse.
are the walls made of dry wall?
what's underneath the carpet?
are the walls parallel?
Slate resonators are generally used to handle specific problems and are not wide bandwith devices. it depends on the width of the slat, percent slat to surface area, depth of slat and depth of area behind the slat. filling the slat resonator will widen the bandwith, but it may be missing the mark.
as you've described the room and surfaces, my estimate is your rooms decay rate is unbalanced at best. I think you have too much treatment (for 500Hz and above), especially with the carpet on the floor and mode problems below 200hz due to room dimensions of 20X24X10. the room can handle frequencies down to 565/24 = 24Hz. but the other dimensions of 20 and 10ft will cause mode stacking. i'll run a calc when I can and post it. also, your slat resonator may not be designed optimally for your room.
