Its a BMW with 235k.... running 20w50 or 10w40 conventional oils with 1qt/3k consumption with 235k miles????? I don't have a brand preference. So, if you can't find your 20w50 conventional Castrol, use any other!
With what I've seen with so-many 40k-70k mile domestics/asian/euro cars burning a quart every 1k miles, I wouldn't worry about your BMW's consumption.
Stick with what you're doing. Keep the intervals sane. Keep the oil level full.
If it were mine, I would consider a 15w40 HDEO, or the 10w40 20w50 motorcycle oils. I use and recommend synthetic but obviously, you don't need it and proved it.
LL might be overrated especially for those with eternal oil change intervals and 1/2 empty sumps. And, if the interval is shortened, why bother?
I would never consider running the oil more than 7500 miles and I don't care how fancy the oil or full flow filter is... enviro marketing has taken over mechanical common sense.