Sounds exactly to me like hard rail clipping from overdriving the op-amp itself and is a reason why I don't like circuits that do that. I don't know of any remedy that doesn't involve a few invasive mods to the circuit, but you can try something a little less complex;
Replace the 1458 with a socket and test out a few different dual op-amps to see if any are better for avoiding the fizzle.
Try a TL072, NE5532, RC4558, and LM358.
Replace the 1458 with a socket and test out a few different dual op-amps to see if any are better for avoiding the fizzle.
Try a TL072, NE5532, RC4558, and LM358.