I would like to replace it with a jfet-based circuit, more "tube-sound-like" because the sound of the BJT circuit is not of much interest.
J-Fet's do not inherently sound "tube like", they have 10 to 100 times the distortion levels of Tubes in a simple common Source/Cathode circuit.
I know, however, that jfets are "capricious and delicate" to implement and I would like to get your advice and if possible a viable schematic.
I do not know who considers J-Fet's "capricious and delicate".
The only issue is that you need to design keeping part to part variation in mind.
I post below a schematic that I found on the net as well as the link leading to it. And also a link to the excellent article on Jfets by Rod Elliott.
I suggest Erno Brobeley's articles on J-Fet's.
https://audioxpress.com/assets/upload/files/Erno BorbelyJFETs The New Frontier Part 1and 2.pdf
I am unenthusiastic about anything shown in the thread so far. But then again, it depends what the goal is.
I redraw the Hampton schematic... but I have a few questions :
- is the 100nF as signal input blocking cap is ok ?
Do not use input blocking cap's. They are pointless.
- is the output at a sufficient low impedance to avoid any adaptative circuit ? it's gonna "feed" a Line In sound card (10KΩ)
The Emitter Follower is suboptimal at best.
* I think 100KΩ at output after R100 is better than 10KΩ (?)
Use 1M even.
I think I forgot a gate-stoper for the 1rst Jfet (1KΩ ?)
J-Fet's normally do not need gate stoppers. All they do is add extra noise.
Revisited schematic below...
Honestly, this schematic and the original Hampton are good examples how not make a design that is intended to be produced or to be built by inexperienced builders. Performance, well....
The J-Fet specified is process 55, which is "general purpose amplifier", where a process 51 part would be a better choice (Low Frequency, Low noise).
See more here:
https://www.onsemi.com/pub/collateral/an-6609.pdf
For most J-Fet's the part number is inconsequential, it reflects marketing, selection, basic performance is down to process.
The JFET specified also has a VERY LARGE variability of Idss or Vgs(off), meaning it will be hard to get the correct drain voltage for maximum output. On top of that it is run at very low current, where the variability is even larger.
The CCS relies on the Beta of the CCS transistor. Seriously? I plugged this into TINA (MPSA14 is a Darlington for which there is no model, but a discrete Darlington with BC550 will do fine) and here is what we get:

The current in the follower is way too high. We probably want around 10mA, not 40mA, but I will tweak the base resistor to get 40mA:
Ok, if we do not tweak the J-Fet Operating condition, what is the result?
Gain is ~26dB. Maybe that is what is needed, but seems low. A single stage 12AY7/12AX7 will have way more gain.

Harmonic distortion for 10mV in and 190mV out is ~0.5%!

I only know one tube that approaches these levels of non-linearity and that is not really a tube, but a VFD abused as gain device (aka Korg Nu-Tube).
If we increase the output to ~1.9V, we get 5% THD!!!!
At 3.8V out we get severe distortion :
Noise seems acceptable at 10mV in with 87dB:

Now perhaps such levels of HD are wanted, to me they seem very high and I am not a fan of low THD as such, but the standards of even a very basic non-feedback tube circuit, this level of performance is absolutely dreadful.
I would described especially distortion performance as derogatory caricature of a tube Circuit. In my view this circuit lacks ALL the true qualities of a Pro-Audio tube circuits and offers nothing of compensatory value. Ok, it produces gain.
It would be trivial to improve the ability of the circuit to be replicated more reliably, about that's kind of besides the point. Here something that is slightly adjusted to ensure it can be replicated reliably:

With optimised operating point distortion can be lowered. This circuit would have to be build and tested to be sure performance is optimised at 8.5V at TP1, but the models in TINA TI are pretty good.
Still the performance is pee-poor by open loop tube standards. Maybe not quite "tube screamer" levels of overdrive, but these levels of distortion will audibly colour the sound.
Thor