I would second trying a tube preamp along with tube DAC, the Lab 12 DAC 1 or something from MHDT, I had a balanced MHDT tube DAC that did make a noticeable difference.
I would still stand by shifting away from your current Amp and to something that is known to drive speakers with difficult loads, impedance swings. In my research, found a good amount of people with real world experience that echoed this, it made the biggest difference for me, gear wise. There is also a lot of truth in room treating but I think you are in the same boat I am, it’s a shared living space and you can only room treat a certain extent before the family will shut it down.
I’d also be weary of anyone making absolute statements, Focal makes amazing speakers, they are designed and built in house, likely one of the if not the top Speaker company when it comes to their ability to scale, making really high quality speakers with outstanding engineering, R&D, craftsmanship and synergy. That said, they have a sound signature, not everyone loves Focals, if you aren’t in love with the sound signature, which does lean into the hyper detailed side of things, even with the room treated properly and the right electronics, you likely won’t love the speakers. That’s why different speaker manufactures have varying philosophies, sound signatures. Take Sonus Faber as a compare and contrast to Focals, in general, if you are a big Sonus Faber fan, you won’t be a big Focal fan. Both are high end speaker manufactures in Europe with Focal likely having an edge due to their vertical integration on just about every component in their speakers but you’ll still have a decent percentage of buyer pick Sonus Faber based on a preference toward a more laid back, warmer sounding speaker. Neither is right or wrong.
I think the plan around using your Yamaha receiver is a great place to start. Do some research on room treatment, you can try some DYI things out form a temporary basis along with using the Yammy, that should give you the baseline to decide if the speakers are right for you and that is absolutely all that matters, your ears, what sounds good to you. When I sold the Electra’s I had was to a new Audiophile, he had nothing but the speakers, I ended up hooking up an old Yammy HT receiver I had, didn’t have Room Correction, he listens to the Yammy, A/B against a Parasound A21 and Primaluna 400 Evo Integrated, he bought the Yammy from me for $ 50 and last check was still using it to power the speakers. If you do keep them and you want to stay in your budget, I would look at used Parasound a21’s, the older version is a really good deal, jump into a used Tube Pre, that combo would work wonders for the Kanta’s and what you are trying to accomplish. You could then upgrade the Streamer / DAC at a later date and the Pre if you got the itch. The Parasound A21 isn’t the best Amp out there but for the $$, used, you will have a really hard time beating the value for what you are looking to accomplish, high quality parts, designed by a legend in the industry, A/B amplification that is beefy and leans slightly to the warm side of the spectrum. I have no bias towards Parasound, I’ve cycled through a ton of gear, I don’t own any Parasound gear at the moment, I did however use an A21 with multiple Focal Towers, again, wasn’t my favorite but for the money and I bought mine new, it from a value play, beat everything else I had, hands down.
Good Luck!