It would not be a bad idea to isolate the meter as much as possible from the audio signal.Since the meter is not in the actual "listening loop" you need not worry about how the input op-amp sounds.
Instead look for something with ultra low current use and a VERY high input impedance.You probably can use 1 meg ohm input resistors and then bandwidth limit the op-amp to 'audio frequencies"
Maybe even a bass cut in the meter response.I seem to remember from past experience with this type of circut the same problem with LEDS always on,but it stopped when I limited the bottom end to 50hz or so.
Matter of fact I think I used the ol' 741 op-amp and used it as a banpass filter with a high input impedance.To do this simply scale the R/C values shown on the datasheet
Still looks pretty cool though
Cheers
Rick