OK, here's where I am now.
The Alpine SWR-1223D 12" Dual 2 ohm, with the voicecoils in parallel. The Qc is a lille higher than with the ideal box, but only about one dB or so, and that should be tolerable.
Amp would be a Polk PA400.1 Monoblock, to do 400W RMS at 1 ohm.
Box as noted...