I am about to embark on my next upgrade journey

I was going to recommend the Alta Alyssa speakers but they are a 4ohm 87db efficient speaker.  They probably wouldn't require a sub based on their low frequency extension.  Good luck.

Picking up on the comments of @jfrmusic I have a pair of Spendor A6R's for sale over the other U.S. Mart that you may want to consider. They are not stand mount but occupy about the same space. They feature a transmission line cabinet and are known for their glorious mids. Paired with your subs, they would be worthy of consideration. The money you save could go toward that streamer, or a new amp or whatever that next upgrade is.

Have you considered the Magnepans LRS + ?  You have the room to pull them out from the wall and you also have to subs to help with the low Hz A good amp to drive them would be the Orchard Audio Starkrimson Stereo GaN Ultra DMC 2.0  250watts@8ohm & 500watts@4ohm  

I would definitely recommend auditioning the Borresen X-Series the X1 starts at $5,500 US and even the X2 is only $8,800 and the X3 is $11,000 and they punch way above their price range phenomenal sounding speakers.

Room correction. I recently added a McIntosh Men220 room correction unit to my system. It dramatically changed the sound for the better. I may do a full on report if anyone is interested. But, one of the big things it did was to align all of the phase and frequencies between my speakers and subwoofers. It adjusted phase and crossover frequencies, making all of my speakers work together. It was also a hit in the WAF, (wife appreciation factor) as my wife can decorate without multiple room acoustic treatments all over the room. 

I own a set of Fritz carbon 7se  MK2 in a smaller listening room with very good electronics (IMO) and a SVS SB 3000 sub. Listen to only Rock, they are so GOOD. I told Fritz during a recent conversation, after listening  for 3 plus hours that I would never sell them. They look so simple and refined, but sound so good. The call was just about telling him How much I enjoyed them. Robert TN

I’ve owned many speakers over the years mostly British made as I prefer their sound characteristics. Recently purchased Harbeth C7es-XD pair. If you want something that sounds like real music with no hype then  Harbeth is a wonderful brand with several models. They all sound musical. 

Since you are asking about speakers, I also recommend Fritz Carbon 7SE MK2s. They fit your desired specifications. A very easy to drive and like speaker. I own a pair and use them in at room much like yours. John, the owner of Fritz,  offers 30 day home trials. I encourage you to give him a call. Very nice Web site also.

I also agree that you could make advances with the improvement of your source. A subject for a different thread possibly.

Good luck in your search.

It all starts at the source.

You're not getting the best out of your system with a laptop at the beginning of the chain.  Get a real streamer.

When I read this post and saw the Sopra 1 mentioned I thought of recommending the Fritz speakers.  So a third recommendation for them.  I recently listened to the Sopra 1 and it has nothing on the Fritz Rev 7 SEs I have.  The Sopra is certainly a bit brighter and does not go as deep as the Fritz.  I haven’t heard the Carrera BE or the Carbon but I think it would be worth listening to especially at less than half the price.  The Fritz has all the attributes you mentioned that you feel are missing from your current speakers.

@upward_bound REL’s designer advocates a relatively low crossover point for their subs, correct?

This might be relevant to the bookshelf model you select, if you are determined to pair them with a specific model of subwoofer. From your OP I can’t quite tell which will be the cart and which will be the horse in your case, but it might be advisable to put the two in the correct order from the get-go, if not choosing/getting both (monitor + sub) models at the same time.

I have heard the Watkins Gen 4 and they are very impressive. He demos them w/o a subwoofer in a room about 15 x 20" with 10 ft ceilings. It doesn’t lack bass in that big of a room which is ssurprising. Its not tipped up on any frequency but very balance and fills the room. Its easy to see why Absolute Sound gave them the accolades they did. I considered them but my room is too big They do have a 30 day $$ back also.

Shop | Watkins Stereo & Loudspeakers, Kingsport, TN (watkinsaudio.com)

I'd second the Fritz recommendation. The Carbon 7's have a hold on folks, for good reason. See, e.g. this and this.

I am not a big fan of the B&W 705 S2. They have poor dynamics and so so highs. The Sopra should be a big upgrade in all areas. The the down side of focal in the US is price, there are a lot of things just as good but cheaper. If you like/want the focal and don’t mind paying an up charge for the name/looks they are one of my favorite stand mounts. 
 

The Revel 226be is worth looking at. It would actually take up less floor space as they are very narrow. They can be had for about 1/2 the price of the Sopra 1 if you shop around. Here is a video demo of the two, of course take YouTube videos with a gain of salt. 
 

In addition I’d recommend taking a look at Fritz speakers.  Great sounding, cost effective and designed for optimal performance with most any amp. 

It is worth taking some time and listening to some different speakers. If you want very musical speakers then I would recommend looking for some used Sonus Faber Olympica 1 or Olympica Nova 1. These are very musical. Focal tends to be really detailed (a bit on the trebly side) and not as well constructed. Sonus Faber… has a very musical / natural house sound, so you can listen to any model and get the idea.