I had to change my keyboard layout from US International to US and I had to switch to a different way of inserting accented letters. I agree with you that it's not very clear why Apple chose their dead keys.
I came up with this mnemonic:
It's based on the completely non-native pronunciation of the Umlaut, accent grave, accent aigu and the accent circonflex .
I could never remember them (and there are a lot more than four). But there's nothing to remember with my macro. Love the thing.
(I may not have pointed this out before but you can also call on the macro in editing to add an accent just by placing your cursor to the right of the unaccented character and pressing the hot key.)