I'd eliminate C9. Some op amps aren't able to drive capacitive loads
without exhibiting instability.

OK, done.

If you're using a good low-noise op amp,
you can probably just omit the filtering here and feed U4's output
directly to your "common".

I'd also recommend decoupling your 16-volt power supply, with a .1 uF
located as close as practical to the V+/V- pins of each op amp.

Sound like basic good advice. :-)

Remember to get the polarities of C1-C7 correct when you install them
(+ to the op-amp side, - to the outside world).

I presumed that such coupling caps should be non-polar. No?

Thanks.