Bird-bomb etching can be tough (or even impossible) to remove.
Noting that these products are discontinued (but still available) I'd start with 3M PI-III MG (05937) and if that doesn't do it then I'd use PI-III RC (05933) and then follow up with the 05937. These are my go-to products before the Klasse twins and they work fine by hand.
I really like 1Z polishes by hand but they leave wax which the AIO will remove, sometimes uncovering leftover marring.