McCartney always has been a composer who had a good sense of music, enough to use the melodic minor scale correctly in "Yesterday", and without knowledge of music theory. But as a classical composer? I don't think he's got what it takes. With his money he could afford the best guidance available but he chooses not to seek it out, or has been told he won't make it and is keeping it quiet. A super-arrogant person.
I know nothing classical of Elvis Costello, recalling that he started out on a contract with Stiff Records many years ago, did a few gigs with same crowd, Ian Drury & the Blockheads, the Damned, etc, and seems to have resurfaced. I'll look him up but any recorded works to recommend?