Any of the speakers would be a good match with the SET 400. I haven't heard the Salk Song3 beAT. My amp is the AVA SET400 with Salk HT2-TL speakers the pairing is magical with plenty of soul.
The Song3 beAT would have the most detail of the three speakers mentioned. I recently listened to the Salk BePure1 monitor with the same beryllium tweeter and it had detail to spare, we thought it sounded best with the grill covers on. The Song3 beAT is probably the best speaker in the group but it may not the best speaker for you. The Song3 beAT
might have too much bass for a 12'x12' room. You listen at low levels so it might not be a problem. I don't know how you would find out, ask in the Salk Circle.
https://www.audiocircle.com/index.php?topic=189729.msg1984959#msg1984959Fritz loaned me a pair of Carbon 7s for a month. We listened to them in three different systems, both solid state and tubes and they sounded amazing each time. The Carbon 7's image like crazy and are not fussy about setup. The Carbon 7 is the speaker to get if setup is not optimal. Plenty of bass too, friends will ask "Where's the sub?" Super easy to drive and sound great a low levels.
In my living room the speakers sounded mellow compared to the HT2-TL that have the SEAS drivers and RAAL tweeter. In Mick's small room the Carbon 7s were alive and rocking. We placed the Carbon 7s on chairs at Larry's house and they disappeared, we loved the sound.

I haven't heard the Philharmonic BMR Monitors. I have read they are voiced toward classical music with a wide soundstage, the result would be less precise imaging compared to the Song3 beAT, Salk HT2-TL and the Carbon 7. There are plenty of Philharmonic reviews to parse to get a feel for their sound. Dennis Murphy designed the crossovers for Salk speakers and should be able to help describing the sound of his speakers compared to the Song3 beAT.