Big Tabs
looking backwards, going forwards
IMO Doobie Brothers were overtly southern rock in the Johnston-era and became more soul/R&B-orientated when McDonald stepped in. A Michael McDonald solo concert definitely has a strong soulful vibe. Steely Dan are a genre unto themselves but the nearest category would probably be Smooth Jazz or Jazz Rock.
EDIT - Wikipedia lists McDonald as "blue-eyed soul, R&B, pop, and rock", I guess that covers it all!
He may be a master of soul and R&B, but classifying Michael McDonald as a rock singer is a bit of a stretch!
It might be a bit of a stretch... but thank you for agreeing that Michael McDonald is regarded as a rock singer. (along with all the other categories you listed)