Greets!
Right, no carpet/padding to absorb the sub system's HF BW, so an absorptive 'phase plug' directly underneath it should help a bit, though it will have to be either have a large area or make it up in thickness to be effective down low. In a typical square/rectangular cab, better to have both the driver and vent bottom loaded to damp them both, otherwise only bottom load the vent, though Sonotube style alignments have some useful pipe loading, so venting out the top and experimenting with damping it to see if it audibly improves its overall performance in-room (AKA critically damping the (sub) system) is desirable.
Best overall for a down firing alignment is a band-pass though as it acoustically rolls off its HF response to create an effective higher order XO slope when combined with an electrical one. Indeed, when properly designed as part of a total speaker system it typically doesn't need an electrical XO if the mains go low enough in a maximally flat (0.7 Qtc) sealed alignment.
GM