Perfromance of ICL7660 isn't unreliable. It does what it's designed for. It's not neccesary to have regulated supply voltage for a good OPamp in certain situations, because these supply fluctuations need not necessarily have to have bad effect on signal integritiy. Power supply rejection of TLC277 is 95dB typically. Means: If power supply voltage is changing by 1V, which is much more than expected, an additional offset voltage of only 18µV is introduced! And even if poorest power supply rejection ratio of guaranteed 65dB is assumed, then an additional offset voltage of only 560µV is introduced.
This is the result of an enormeous amount of internal circuitry of OPamp, circuitry that stabilizes idle points by the help of constant current sources, zener references, etc.
And don't forget 100Ohm plus 100µF filters. These will eliminate any high frequency ripple coming from ICL7660.

Performance of ICL7660 should not make trouble in your application. Situation would be different of course, if a resolution of 12bit or higher was wanted...



When you furtherly want to use TLC277, then supply voltage should be reduced a bit. Maximal 16V should be present on supply pins. This could be managed by using +-8V supply. Then, 16V zener diode should be omitted.

Another option is to choose another OPamp, like your TL084, or better TL052, which is much more precise! This would work with +-9V supply.

Kai