Integrated amp for Philharmonic BMR monitors

yep low efficiency and lowish impedance through the bass and lower mid region

go for more power as long as the watts are clean sounding

One of my friends uses Audio by Van Alstine tube pre and ss amp and is really happy with the sound.

I know someone using the BMR monitors with a Hegel H190 integrated, he loves the results. I recall him swapping out a few different units before he landed on that one. I think it was a Gato Audio with a Class D amp section, a PS Audio Stellar Strata, a nice Unison Research that wasn't quite powerful enough for bass impact, and an Atoll EVO200 that was surprisingly capable. The Hegel ended up being top choice though.

This is somewhat tough. Because the BMR is somewhat inefficient, lower cost low watt amps are excluded. At this price level, more power including more current costs more. 

The entire audio chain matters. It’s best to strive for a balanced system as generally the Sonics are only as strong as the weakest link.

The OP’s budget seems to be 1.5-2k, but the sonic bargain BMR can significantly benefit sonically from better amplification but at a higher cost.
While a used Hegel H190 may be a good stretch choice, a used H390 is significantly better sonically and their optional DAC is very good.

Maybe a 2 box option: Schiit Wotan amp + a preamp