I doubt the ripple measurement is correct: At the switching node the ripple should be almost 6Vpp, so 240mV is most likely wrong (or something else in the circuit if the 240mV are correct).
A 555 will also produce some ripple on its supply voltage: Not only due to the charge pump but also due to cross conduction of its output drivers.
I should have added "measured with an Uni-T" disclaimer...
I think I am more measuring the charge/discharge cycle of the 47uF cap than any 555 generated noise. With a LED plugged there, I kinda sorta subjectively see a slight shimmering.
On the -3.04V and the -2.65V, I can't see this shimmering at all (if that has any value...).
As a side note, I have a 380V to 240V system in my house, and a 230V at the Uni, I have slightly different results.
The Uni's 230V works best, and that's where I'll be deploying the sensors anyhow.
With careful design your 1.2 mV ripple should be fine. Look up the power supply ripple rejection in your OP amp spec.
That's the value of AC current in mV detected by a Fluke 175 and a Uni-t - not the best way to measure, but that's what I've got.
This ripple is really at the limit of what I can detect without an oscilloscope plugged in. But I've got the finish an Apple G5 open heart surgery to get space on my desk...
So it could be double that or half that. But I think the culprit is the ground on the transformer, but a simple LC filter should deal with 90% of that (to the point where it's irrelevant).
The pressure sensors I'm using have a bout a 20mV range before amplification at 3V, I'm going to see if that improves with 6V...