"I nearly always have to fine tune afterwards by ear."
Then you most likely have a crappy electronic tuner....

" I just wanted to minimise the number of gadgets I have to plug in"
So that way when one breaks, they all break (And they will break.. anything that gets used, wears out....all it takes is time)

Come out of your guitar into a decent preamp, and from there to a Boss TU2 peddle tuner.... when you click it to tune, it can kill the signal to the mains....

2 pieces....

easy sneazy

:-)