A list of efficient speakers at ~$5K a pair.

Hi mesch my room is about the size of yours 11x15.5x8. I have Charney Audio Companions with Voxativ AF2.6 drivers. These are out of your 5kish budget but the Charney Maestro and Maestro X with Voxativ AC 1.6 drivers will fit your room and budget. Brian came by one day with the Maesreo X and I must say I was very impressed with what I heard. Both Maestros are made for a smaller volume room and the bass might lack a little. The sub of choice is the SVS 3000 Micro. 
FWIW no sub needed with my Companion Voxativ 2.6 combo. Very musical, engaging and real. Look into them I think you’ll be happy you did.

 Charney Maestro

Reference3A.

Makers of two way systems where the mid-woofer rolls off naturally, no crossover needed.

My DeCapoI speakers are rated at 90db and have a reputation for benign impedance characteristic.

Not to mention they should glorious!  I drive them with a 25wpc OTL tube amp (in the winter only, way too hot here in the summer for tube amp)

Tekton Moab. 98 dB at 1 watt. Very full range, especially with the added, single per side, Be HF driver.

I'll third the De Capos. run them with a 4 watt tube amp and plenty loud but the sound is so nice rich but detailed

I think the reference 3a Decappo would be a sideways move against your Fritz and you might prefer the Fritz, I own a pair. Try the Ref 3a Reflectors 92 db 8 ohm they are a total different speaker but same flavor as Decappo. It’s just a speaker that could help end the chase, used you could pick up a pair in your range. I run them with a 50 watt class A tube amp.