Audio Note speakers

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.

To all here raving about AudioNote speakers I will point out that they are copies of the original speakers designed and manufactured by Peter Snell (RIP) in Massachusetts. Yes, the crossover parts are more costly but the overall designs are the same.The original Snell’s are available on the secondhand market for a fraction of the excessive prices charged by AudioNote. I have original Snell Type A’s, E’s and K’s. When you buy AudioNote you are paying for a marque name - not better sound compared to Snell.

I bought a pair of the original Snell E's a while ago and was not impressed. Sounded like the medium size boxes they are. And I like vintage speakers- replaced them with similarly scaled Monitor Audio MA-3's, which are a huge improvement. I find it really hard to believe Audio Note An-E's would win any fans at all if they sounded as "meh" as the old Snells that passed through my hands. Perhaps the caps in their crossovers were old, or something of that order. I have some breadth of experience with vintage speakers. Keepers: Quad ESL 57's, ADS 810's, Altec 604G's in 620 cabs, the MA-3's mentioned above. Out the door: Klipsch Heresy II's, Cornwall I's, Vandersteen 1C's . . . and the Snells.