I finally was about to bite the bullet and order an Eonon unit for my 2001 E53, and it seems they don't offer it anymore..:
https://www.eonon.com/Car-Type/BMW.h...QaAof_EALw_wcB
Now on eBay, there are many products, including the Eonon for E39, that make comments in passing about being compatible with E53:
https://www.ebay.com/itm/For-BMW5-E3...sAAOSwimdgFhrS
(E53 is mentioned in the title, but nowhere else in the compatibility!)
https://www.ebay.com/itm/For-BMW5-E3....c100752.m1982
The above ("Hizpo"?) looks like the Eonon unit.. But only $218 *(shipped from Hong Kong)
I really want something straighforward to install in my 2001, no DSP, no Navi X5. Main aim will be a reliable headunit, retain the steering wheel controls, RDS radio, and song / podcast info on the screen when bluetooth streaming..