My confusion is also due to the fact that the ECC81 is used as CF for his high current performance, so I was wondering if inserting it in the circuit without mods will give an increase in the current available at the CF output
What will you do with extra current?
Trick question, because you don't really care about the circuit's current output. What you do care about is the cathode follower having a nice low output impedance to drive long cables easily. An ECC81/12AT7 has a lower plate impedance and more transconductance (Gm) than an ECC83/12AX7, so it will result in a cathode follower with a lower output impedance. No circuit changes are necessary (though I suppose you
could change some things if you needed ultimate performance from the ECC81, but it's really not necessary in a guitar amp).
The proposal of Mr. Merlin of a good CF send circuit using ECC81 is very different from the arrangement on the previous schematic (in which an ECC83 is show)
It's only different in the details, after you know what you're looking at.
Look at the first circuit you posted.
Pretend the cathode follower is a Fender split-load inverter without a plate load. The 1M grid resistor is returned to the bottom of the "cathode bias resistor" instead of ground, with the cathode load between that point and ground. The cathode load in this case are the 10k + 47k resistors, in series.
The "cathode bias resistor" is an LED. When enough voltage appears across the LED, it will turn on and conduct, and will flow as much current as required to maintain that voltage. I don't know enough about LEDs to tell you without looking what voltage a red LED conducts at, but we can guess it's between 1-2v. The fact it will maintain this voltage for any reasonable current means it acts like it is a cathode bias resistor with a bypass cap; so you use 1 cheap part instead of 2 slightly more expensive parts.
Now this effects loop is probably placed late in the preamp circuit, maybe right before the phase inverter. The signal level is big compared to a guitar's pickup, and you're probably using effects pedals in the loop. So along with a low output impedance, you need to drop the signal strength. This is done by dividing the cathode load in 2 parts; the output in this case is about 1/6th the input to the cathode follower, and then has a pot to allow you to reduce the signal further if needed. A coupling cap keeps d.c. at the cathode load out of your pedal's input circuit.
On the Return side, there is a virtual earth mixer, as you noted. Both signals are mixed only if you have selected the parallel loop setting. In essence, this tube is being run as an operational amplifier (opamp), and the gain of the stage is determined by the series resistor and the feedback resistor. The feedback resistor in this circuit is 1M; The series resistor for the Return jack is 10k, with 100k for the parallel path. The gain is 1 + feedback/series resistor, or 1 + 1M/10k = 101 for the return jack (really just the gain of the ECC83 at around 50-60, or essentially no feedback) and 1 + 1M/100k = 11 for the parallel path. That's because the return jack has an output at pedal-level, and needs to be boosted back up.
Which is why Merlin recommends a ECC83 or ECC832/12DW7 for the loop; you need the extra return gain, though the low output impedance of the 12AU7 as a cathode follower might be helpful.