That’s quite memorable. On the Mac I have to press option-u and then a, u, or o to get an ä, ü, or ö. Optionally holding the shift key to get an uppercase vowel with the diacritic.
option-` is for grave (è) option-i is for circumflex (é) option-n is for eñe (ñ) option-c is for cédille (ç)
When you called QWERTZ an abomination I simply had to upvote your comment.