Sweep Picking, concerning 12th fret Options

[fire]

hi guys
here comes my question( i really need help -.- )
I'm not having troubles with sweeps anymore, so thougt I -
but - well, heres my problem:

my guitars strings are very very low and if i have to do a sweep
(that looks quite simple) like Eminor shape
and on the 4th string, i have to play 12th fret with my index finger,
so basically i cant mute it with my left hand, nor, if going down ( upstrokes)
with my right hand. So whats the problem?
When im coming down the arpeggio and going off the string, it rings => natural harmonic, but
still when i keep touching it, there's a n.h. - i cant prevent it from ringing - i can make it last very short,
and i can make it be less loud, but i cand avoid it 100% - any help???

thanks guys!!!

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