From there it's simple to rotate if any of the vowels get picked up into words with common non-vowels like S and T etc.
If no vowel appears out of OUIA, I always go for a word like STREP.
Becomes relatively trivial from there.
Today (01/13/2022) the word was ABBEY.
I'll represent GREEN squares with * and GREY squares with ^
It went as follows:
OUIJA^ B^E^A^ST FA^B*LE^ ABBEY
After FABLE, the first word I could think of that had at least 1 A, at least 1 B, and at least one E was ABBEY.