-Can this be done (the Nick Gammon method), but using directly an AVRISP MKII instead of using the arduino as ISP?
To be clear, NG's method is a sketch running on any arduino board, then wired to a target arduino board. No other programmer is or needs to be, involved. Nick's sketch is pretty intelligence in that it reads the target board's signature bytes so it knows which bootloader to burn into the target board as all the popular bootloader hex file data are already embedded in his sketch. It's a standalone solution, The IDE is then only used for it's serial monitor so you can interact with the sketch, answer questions and see the results.