I'm a big fan of ID speakers...but when JBL is available at a 60% discount and they happen to fit your needs, that becomes a game changer!
I agree with this. I also compared the AA's against the 340's and preferred the sound of the AA's. The 340 should get louder, but the AA's are no slouch. I didn't mention this because you seemed pretty set on the Ascends (or Hsu) and I do consider them good options.
However, I personally would take it up a notch! Given the money you will save on the surrounds/brackets, I would suggest you skip the center and get a pair of SVS Ultra Bookshelf Speakers. They sell for $1000/pr, but if you check the link below periodically for B-stock, you can save some money (read where they describe the blemishes - some are open box with no damage and others open box with some sort of damage to the finish). Right now they have one with no damage for $450 and another for $400 with a crack in the bottom surface - that is a great deal! Don't worry, SVS is careful to make sure there is no structural damage and is is typical for people to buy their B-stock and not be able to find the blemish they describe unless you take it into the sunlight!
https://www.svsound.com/collections/outlet-specials/type_speakers
https://www.audioholics.com/bookshelf-speaker-reviews/svs-ultra-bookshelf-speakers
My reasoning is simple:
1) 45 day no-risk trial is assurance if you don't like the sound (I can tell you they are excellent speakers for the money, but cannot know you like the same sound character as I do).
2) These are SVS's flagship bookshelf - often companies use their top of the line products to make a statement about their capabilities, and they put extra emphasis on making sure they do not disappoint! These don't! I have not heard any of SVS's lesser speakers, but know people who were not too impressed with the Primes, yet considered the Ultras truly great speakers!
3) I have heard these speakers and to my ear, they do everything very, very well. Another way to put this is: these are speakers that I cannot find fault with! I have better speakers and I know that from listening to them side by side with instant level matched switching, but if I leave the room for 15 minutes and just listen to these by themselves, they do no wrong! In my book that makes them true high fidelity speakers. If I listen to the 340, I will notice that the highs are not as crisp and transparent as they should be (can be heard with the brass of the metal strings in the intro to Hotel California from the Eagle's "Hell Freezes Over" album as a commonly available example).
4) I always advise getting two great speakers over three good speakers across the front. Your AVR will automatically configure for a "phantom center" when you run the setup. You can try it out as part of the 45 day trial, but with great speakers, I think you will be very content with the sound. Should you decide later to add a center, I would suggest simply adding another Ultra bookshelf instead of the Ultra center. The center is very expensive ($700) and will not match the timbre as well as another bookshelf. The only reason they make the center is for a low profile (8.2" high instead of 15") which allows you to squeeze it under your TV. It just depends on your furniture and whether you can fit the extra 6.8" to save $200!
All of that said, I don't remember - is this primarily for HT or music? Did you give us a %Music/%HT/%Gaming breakdown on your listening habits?