By general audience, do you mean any book that's not intended for academics?

Yes

I'm an avid reader of history books (antiquity, middle ages), and I'd say I'm very picky, trawling through reviews and recommendations from trusted sources before deciding on a book.

I have already come across books that were a slog to read because of the author's simplistic worldview or obvious contrarian agenda (so I can definitely relate), but I've also read some masterpieces (for example, Kaldellis I believe is solid).

Unfortunately I don't count any historians among my friends, so I'd welcome any recs from you for authors that are the least bad, or a teardown of main antiquity/middle ages historians.