Giorgio,
Thank you for your post.
In short, no. The TLP can never quite match the GK-1.
Reason: the GK-1 has a differential power supply circuit which draws constant current from the power supply at low frequency. This means that as the signal output slowly moves up and down, the counterbalancing power supply shunt element moves down and up, and the currents sum to a constant. This gives very tight bass and a perception of speed and agility which is difficult to match with any other design.
However, this counterbalancing power supply principle reduces the emotional engagement at the middle and higher frequencies, so it is progressively reduced with frequency so that by 10KHz the audio tube is fed from a high impedance power supply, giving that marvellous tube romance we love.
The TLP does not have this additional circuitry. It's good, but the GK-1 has imaging, bass and dynamic qualities which are clearly much better.
I hope this explains the difference. It's not so simple!
Cheers,
Hugh