As far as I know, the first three B.B. King quad releases (1971's In London and L.A. Midnight, and 1972's Guess Who) were all single-inventory QS quad, most likely thanks to the involvement of Ed Michel, who produced the first two and probably oversaw the mixing of the latter one thanks to his role at the top of the food chain in ABC's engineering department.
After that I think it's dual-inventory for 1974's Friends and Together... For the First Time (with Bobby Blue Bland).
Both 1973's To Know You is to Love You and Friends were recorded at in Philadelphia at Sigma Sound (probably best known for its association with Philadelphia International Records) with studio owner Joe Tarsia engineering. I spoke to one of the engineers that used to work there and asked him if he had any recollections about the B.B. King quad mixes - he said he remembered a QS encoder being brought in (they were already set up for SQ for the PIR stuff, and CD-4 for the Atlantic quad mixes like the Spinners they did) for some of the B.B. King mixing but he couldn't remember if it was for To Know You is to Love You or for Friends so I was unable to get any verification as to whether a quad mix of To Know You was ever done. Personally, I don't think it exists - despite being rare, all the other B.B. King Q8's have shown up from time to time and I think that one would have surfaced at least once in the last 40 years.
As to the rarity of the tapes, for me the B.B. King Q8s have been some of the toughest to find, especially in anything approaching very good condition. I attribute this to a combination of blues being somewhat of a niche genre (relative to rock and roll or easy listening) and also toward GRT's distribution network not being great compared to the big boys like CBS and WEA, and probably also to the fact that my cheapskatery won't allow me to spend $50 a tape for these titles. The fact that GRT was bankrupt well before the end of the 70s I think says a lot about how poorly their sales were doing, and I'm sure quad was probably an even smaller part of that picture.
If you're interested in King's output from this period, I highly reccomend checking out this BBC Documentary about the recording of In London called 'Sounding Out' from 1971 that someone has kindly pirated on to YouTube for your viewing pleasure:
As Wikipedia notes, King "is accompanied by US session musicians and various British rock- and R&B musicians, including Ringo Starr, Alexis Korner and Rick Wright (not the same from Pink Floyd), as well as members of Spooky Tooth and Humble Pie, Greg Ridley, Steve Marriott, and Jerry Shirley" and lots of them appear in the documentary.
Also interesting from a quad standpoint is that the album was recorded at Command Studios, at 201 Picadilly, right in the heart of central London. The studio was short-lived, but it was one of the first quad equipped studios in the UK (you can see four of the quad joysticks for panning stuff around the quad soundfield on the mixing desk at 17:13 in that video) and it's where the unreleased quad mix of Pink Floyd's Echoes was done the same year.