Audio Note speakers

I really like the AN-J speakers too.  As Jond mentioned, the paper cone speaker is slightly warmer sounding, but the difference is not that big and both sound very good.  I don't know about your specific LTA amp, but the ones I've heard are slightly on the leaner side compared to Audio Note amps so it might make sense to stick with copper speaker cables, particularly at any reasonable price level.  I like the Audio Note cables but I've also heard the AN-J's with Acrolink copper cables and the sound was very good.  

Good friend runs AN-J’s as well, he drives them with AudioNote’s Cobra amp. That is a wonderfully musical system. Great synergy. All the more expensive versions of AN’s speakers run the Hemp drivers for a reason they are more detailed and musical from my experience. Get the best ones you can afford. I would also consider the AN Cobra amp as another alternative to the LTA, the synergy is there with he two. The Cobra-AN-J is a combo I could easily live with forever. Oh and the DAC in the Cobra is surprisingly good.

I owned the An-J’s for 2 years, and had both paper and hemp. Martin Grennall at AN advised the hemp because he feels it’s richer sounding. I think if you prioritize tonal richness and fluidity, hemp is the correct choice. If you prefer dynamic articulation, paper works better. 
I sold my J’s and upgraded to the E’s, which provide significantly more satisfaction in my space. I’m not sure of the size of your room, but the body of the music, the bass, and the power all increase in quality and size with the E’s. They work remarkably well in small rooms, and I cherish their ability to fill my space effortlessly with a wall-to-wall hologram of sound vs the J’s more dainty projection. It’s a difference experience, and which is better is subjective. 
regarding your LTA: I haven’t heard the Z40. I’ve heard the microzotl drive my fathers ls3/5a speakers, and he’ll soon have AN-K’s to test, but my impression of LTA is a precise, light, airy sound quality, which I imagine would pair quite well with AN speakers. I’ve owned the AN Cobra and now own the P3 Tonmeister, but have tested Pass Sit 4’s, which may offer a similar sound to LTA, and they sound excellent with AN speakers… less warm and fleshy than AN amps, but pure sounding - clean and clear. 

So I’ve had both the paper and hemp in the same pair of Audio Note Speakers, my AN-E LX Signatures.  At the time of my purchase - nearly 15 years ago? - my dealer favored the paper for their richness/warmth.  Alas, I had a cat incident that wiped out one of my woofers; I consulted Audio Note directly, and they recommended the hemp to replace the paper because it “gives you a much cleaner decay and allows you to hear further into the soundstage.”  They were right; the hemp improved the speakers.  They’re still warm, but the hemp is more transparent.  But you can’t go wrong either way.

I owned AN-E LX speakers with paper cones and now own AN-J speakers with hemp cones, silver inductors, etc. I have used a variety of amps with both. I would guess that the paper cones will be a slightly batter match with the LTA’s OTL sound, but the higher you go up the AN line, the less grain you hear. If you switch to a SET amp or a higher end push pull amp at some point, that absence of grain will be more pronounced. Basically, the paper cones might give you the sound you want now for less $$$, but the higher end hemp and silver speakers will give you a higher ceiling for upgrades down the road.