Are you aware of the related Fast Play supplements?
Yes, in addition to those four, there was also a
Diablo II edition of the Fast-Play game, a PDF-only
D&D: The Movie Fast Play release and
Caves of Shadow which isn't labeled as "Fast Play" on the cover, but talks about itself as "fast-play" inside. (The last two were loosely based on the 3.0 rules, and were included in the 3rd Edition Collector's Guide.)
As I recall, the rules of these and the '99 D&D Adventure Game were derived from the AD&D 2nd Edition rules, not the OD&D/BECMI rules. They also had a relatively self-contained setting, though I don't recall the details.
Ah, yes, the 1998-1999 period where WotC had decided to merge D&D and AD&D under one "D&D" brand but hadn't yet fully committed to it

.
The 1999 D&D boxed set would definitely fit better as an offshoot of AD&D2 than BECMI D&D. (Trivia: It's also the only D&D product to include "Vampire, Lesser" as a creature, as well as the "Xvarg". In case you are wondering, xvargs are exactly the same as xvarts, just spelled differently, because, hey, that's a word than needs fewer common letters...)
That boxed set might well move into the "Miscellaneous" section of guide #20, when I get that far.