This thing crossed my mind and could be useful when learning new kanji Onyomi reading (at least for me).
For many kanji, the onyomi reading is based on one of the radicals it is composed of. For example 官,管、館。Why not adding a note at the end of the kanji reading section saying “Note: this kanji has the same pronunciation than the radical xxx”.
There is no need to change the already existing mnemotechnic but just adding a note can help.
I saw this radical pronunciation link was done for the kanji containing 工 but only them (to my knowledge).