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?
No. A schwa is a schwa. It's the other "systems" that can be confusing and ambiguous. I was just saying that the same sound in UK and American General English is represented in two different ways, the former with er and the latter with uh. (The most famous example of this is in Winnie the Pooh where the reader is admonished that it is not "Winnie thge Pooh", but "Winnie ther Pooh". Most folks from rhotic dialects end up pronouncing the second ther as /ðə/, when the author clearly had in mind the second of two possible pronunciations of the, i.e., /ði:/ and /ðə/.
Are you saying that you do not pronounce the first a in asseverate as a schwa? What do you pronounce it as? FWIW, the OED online gives the pronunciation (in IPA) as /ə'sɛvreɪt/. The first syllable is clearly a schwa.
