"I sawr a behd turday."

That would be a Scouse accent...especially if by "behd" (bayyyyyd...drag it out for about 4 seconds) you mean "bird". Recall John Lennon in the Beatles' "Day in the Life": "I sawr a film turday, oh boy,...".

So is this schwa stuff telling us that the same /ə/ symbol is used for entirely different vowels? That's kinda confusing, is it not?