Not sure what Daddy was on about (as so often), but *'Angelos' is obviously not a real word.
dulcinea, you're also right that it's not a long A as in angel, change, range
but a short A as in Angela
(English!), banjo, flange.
No idea where the German broadcasters got that from. Maybe they were just trying not to say a short E (as short A is so often rendered by German speakers) and overcompensating somehow.
You're also right that the last syllable is not a long E as in lease, lees
but a schwa, or perhaps a short I. No idea, actually, where British broadcasters got that from either, but I agree that it's a BE quirk. (Sort of like saying 'Californian [sic] wine' instead of 'California wine.'
With all due respect, dude, I'm not sure you have much of a clue about real Texas accents. What you're describing sounds more like Hollywood, maybe the Beverly Hillbillies; you might find a few people somewhere who say it like that, but it's definitely not widespread.
Anyway, the pronunciation is exactly like the English word 'angelus,' which you can listen to an audio clip of here at American Heritage
online, or probably also Merriam-Webster.
There should actually be a thread on exactly this topic in the archive. Saying much of this same stuff, in fact.