Hi,
Your circuit should work.
usually audio inputs are high impedance. Thus they don´t stress an OPAMP. Therefore one single OPAMP can simply drive three amplifiers.
No need for double buffering.
Three individual OPAMPs for three amplifiers are useful only if you expect some noisy/distroted feedback from the amplifiers... and you want to avoid the influence to the other amplifiers.
The risk is very low in my eyes, one NE5532 should be able to suppress any unwanted (usual) feedback.
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If you want to stay with the 4 OPAMP design:
Then I recommend to configure all 4 as "inverted" Opamp circuits. This is more "audiophile" because it generates less distortion and give a better step response / less ringing.
Klaus