I don't think you can go wrong with any of the products you've mentioned. BAT has an excellent reputation for great sound and build quality, backed up by service that's tough to beat.
If you like slim, accurate, and excellent soundstaging speakers, take a look at Totem's Arro (around $1000 new). I've heard them with both a Jolida 300B integrated amp ($900 new) and McIntosh separates (total about $8000 new) and the Jolida crushed the McIntosh in providing an absolutely amazing soundstage. The Audio Physic's will have more "slam", but I urge you to try the Jolida/Totem combo. Besides, for less than $2000 for BOTH speakers and amplification (and that's purchasing new), it's hard to complain.
For amplification, you might also consider a used Plinius 8200 or Arcam A22, as they will both fit into your price range.