best WOOFER ???

TAD makes some excellent 15" woofers that have free air resonances in the mid-low 20s.

They sure do! TAD are among the very best.

How do the latest field coil woofers, like those used in some Shindo speakers, compare?

Johnk...Years ago EV made a 30" woofer, but no one tried to put it in an enclosure. It was usually ceiling-mounted working into an attic.

Mapman, the new field coil 15" woofers in the Classic Audio Loudspeakers are also really impressive. They are faster than the TADs, more efficient and have similar low end response.

Eldartford your right many do get mounted in wall. The new super woofers been changed enough to work in massive ported cabinet. Or even OB. These woofers are fast and produce detailed bass with massive subbass at very low distortions compared to small woofers. And even a 21in woofer looks small next to the 31.5in. So get some ply for baffle, cut hole in wall, frame out and you have a super woofer for both rooms;)