I am doubtful that the O2 sensor or fuel regulator are the problem if you are perceiving a symptom only under hard acceleration.

When you say it stalls and cuts out, do you mean it goes for a second or two without firing at all? If so, replace fuel filters. If the problem persists, it could be a fuel pump so follow up with fuel flow and pressure tests.

Does it matter how full the fuel tank is? There is a hose in there that degrades over time.

If it just sputters under load and high RPM, that can be a symptom of a weak spark. Check for a strong blue spark while cranking. Weak yellow spark is not good enough. Check the condition and and resistance of your plug wires. Should be smooth and about 1000 ohms a foot, as I recall. Look under your distributer cap for teltale cracks and evidence of spark going where it shouldn't. Make sure you have full voltage to the computer while running, and a strong signal to primary side of the coil.