Harbeth 40.3's. Should I buy them?

Regarding the X3's, I shouldn't be running subs according to the manufacturer of my integrated. I currently use RCA's spades at one end and resistors on the other inside the RCA jacks. I do not have preouts on my integrated.  But I'm told that's a bad idea for many reasons. I need to stop that practice.

The foundation is really important to the music genres we enjoy. The reality starts to set in when I look at the 'big picture'. I picture a speaker with adjustable bass, woofers, preferably, almost certainly self-powered so that my tube integrated only see's the mids and tweets. I know by experience too that my wife likes a very dynamic picture. I do too. The speaker has to play Radiohead, Porcupine Tree, Shiny Toy guns, as well as female vocals, electronica, jazz, blues, and classical if it can pull it off. My experience with classical is that only big speakers with lots of drivers can pull off the scale of classical. Well, maybe horns too. I know most will disagree but that's been my experience. 

My room is pretty good. 15' x 19' dedicated with GIK bass traps and acoustic panels at the front, 1st order reflections taken care of, Cement slab, thick carpet, rockwool on one wall,  LCR panelboard but a dead back wall as it's nothing but shelving holding vinyl. So no 'live end - dead end'. I don't hear bass issues with any of the speakers in that room not that they don't exist of course.

Swarms are the best way to get a good bass response, fully agree, but I don't have that option. Another reason why I keep thinking that the Legacy Audio Focus XD's seems to check a lot of boxes.

Regarding the X3's, I shouldn't be running subs according to the manufacturer of my integrated.

Start with speakers, then the amplifier. If this is the truly the case according to your amp manufacturer, imo the amplifier is a limiting factor - given all lf the different speakers you've tried and still plan to. Same issue, you'll want to hear the Legacy with your integrated.  Not their amps.

A close colleague went and demo'd them, he walked out being led to believe he needed to buy much higher power SS amps to get the most out of the Focus XDs and a few others. Was told his 60w mono tube amps wouldn't cut it. Bailed out.  

With a really good preamp, with two sets of pre-outs, the right mono amps, the right subs, guarantee without a doubt those X3s could be made to sing. :) my .02 cents. 

You must be talking about adding additional subs to the onboard subs of the x3? Not sure why that would be needed, the bass performance of this speaker is the best thing about it. 

We're not selling our Allnic gear. Not an option.

Our Buchardts are a 4ohm 88db efficient speaker. The Allnics 60wpc in triode drives them without complaint. The 150wpc in pentode drives mode them louder still. 

The Alta Audio Alec's are 93db efficient. They were driven to thunderous levels with the Allnic. 

The Legacy Audio Focus XD is 95.4db efficient and has built-in amplification for the woofers.

I can't believe even 60wpc in any tube amp wouldn't drive those speakers well.

The X3's were not a problem in our room with 60wpc in triode mode nor were they a problem of course with 150wpc pentode mode. I really like them. I've written glowingly about them. One of my dear friends and audio guru, without me knowing, bought the same speaker! I've even got caps for a planned X3 upgrade. My wife never warmed to the X3's and is willing to work for another speaker, even if it costs more. God Bless her. At least she shares my audiophile spirit.

The strength of my tube integrated does not lie with driving 4 x 12" built-in woofers but it probably would. In Legacy form, a built-in 750watt ice module would perform that function just fine, actually, much better and the digital control it would have on top of that in terms of dialing it into one's room may be icing on the cake. There are many options with those particular speakers. I think of it in a way of having very fast subwoofers that were/are already well-integrated a speaker and not having additional subs I can't use with our integrated.

The problem is, there are so damn many nice speakers out there. (like it's a real problem)

It took me 10 years to find the right speakers. Finally got Harbeth 30.2 40th anniversary - My room is not big enough for the 40.2. 

Awesome, was worth the wait. Harbeths are unassuming at first but as others mentioned, you get to appreciate it more and more over time. So natural and clear. Very versatile, except may be for hard rock.

My Pass Lab x25 is a match made for heaven for this speaker and I also agree that an amp with some power depth, like this class A will bring the Harbeths to life as their db  sensitivity level are low compared to other speakers.

Let us know how they sound in your room. Good luck!