He was so frustrated that shortly before his death in 1950 Shaw put the creation of a new alphabet in his will backed by grant in aid. And thus the Shavian alphabet was born. Enjoy:
How about this (equally unworkable) idea to achieve the goal of fixing the disconnect: instead of reforming the spelling, reform the pronunciation. Keep the writing as it is, but pronounce it to the rules (mostly: the letter/multigraph to phoneme map) which you find naturally in the majority of the other languages that use the Latin script. One can argue over the precise details and exceptions.
The good: it makes English much more regular and amenable to learners, all English speakers more or less affected in the same way The bad: the change is drastic so that movies from the time before reform need subtitles, pronunciation will start drifting apart soon and undo the reform efforts quickly
Edit for thoroughness