Alternative to my P3ESR

Have you considered that the amp might be the issue? The worst amp pairing I had with 2 different Harbeth models used KT 150’s.

What SS amps did you try?

Get a Schiit Loki EQ.

I have a setup similar to what you described, but am powering my P3ESR SEs with a Simaudio 600i.  I have a Power Sound Audio S1500 subwoofer (which is totally overkill) crossed over at about 80hz.  I don't feel like anything is missing throughout the frequency range. 

I recently had the P3ESRs in my main system (PS Audio M1200 amps / Herron Audio VTSP 360 preamp) and had some friends over.  They were amazed at what those little speakers could do in my large room.  So was I.  I had them about 8 feet from my listening position and augmented by 4 subs.  They of course run out of gas at higher volumes in that situation, but the imaging, soundstage, and tone were all incredible.

Alan Shaw says that they will run with just about any kind of amplification, but they like power and do well with solid state power.  I have the P3ESRs close to the wall with 4" thick absorption panels behind them.  I have gone through a lot of speakers, but the Harbeths while not perfect for my main system, are perfect for the small system in this room which is probably about 12' X 12'. 

I never say never, but I don't anticipate parting with them anytime soon.  I would try some better SS amps, experiment with crossover points on the sub, and try some room treatments before getting different speakers.

I agree with @big_greg on the amp pairing.  If you read the measurements section of the Strereophile review he mentions how using a tube amp could compromise the sound in the direction you’re hearing.  Basically your amp is not an optimal partner for those speakers and they’d likely do much better with a more powerful solid state amp. 

I have a pair or Proac Tablettes, similar design (sealed versions).  I have a Rega Io driving them, and this amp seems designed for these speakers - it emphasizes the mid bass, brings a fullness to it.  A lot cheaper alternative to try before swapping speakers.  Also, as others have said, since this is a near field set up you may very well be at the mercy of your inherent boundary situation, whatever it is.  Other speakers may have a similar response in the same spot.  You could try DSP.  Lastly, if you haven’t yet, try some EL34s in that amp.