not really. There is the Parity Swap procedure but that only applies when simultaneously upgrading parity and replacing a failed data drive with the old parity drive, but since you want to keep all drives that does not apply.
If you use @JonathanM approach but avoid formatting any of the ‘unmountable’ drives until the parity build has finished the old parity dtive will be left unchanged to give you a fallback if something goes wrong. Alternatively you could simply not assign the old parity disk to the array initially, and only assign it after the new parity is built but that would take longer as the old parity would now need go through a ‘clear’ operation to zeroize it when adding it to the array.