I have a suggestion. In cymraeg (the language of Wales) many English words have been adopted into the old Celtic tongue. To do this they begin with an alphabet that is completely phonetic, as in every character is always pronounced the same, then they simply spell the word so it sounds roughly the same as it does in English read aloud.
We can create our own in this manner using using unique characters from any existing language, Cyrillic even, though I highly suggest we keep it small for simplicity sake, perhaps around 24 characters with no duplicate sounds.

Welsh alphabet:
a b c ch d dd e f ff g ng h i j l ll m n o p ph r rh s t th u w y