DC Power supply voltage swing when load turns on
Your first graph shows a ~70 mV change on a 24 V supply. That's 0.3% variation. You don't have a vertical scale on your scope plot of the 12V regulator, but if the magnitude of the changes is similar, there's nothing to worry about. Neither your voltage reference nor your amplifier should be bothered by small changes in the supply voltage. Is this a noise issue?

Do you have capacitors on the voltage reference and amplifier's supply rails?
Are you able to power the 5V regulator directly from the 24V supply? The heater probably draws a lot of current, and switching that will add noise to your power rails.
What are the supply currents?