You could always try to a find an AD&D 2E game or other older D&D edition. Just advertise as such that you're looking specifically for those editions.
To be totally clear, is AD&D 1e/2e just another name for D&D 1e/2e, or is it a variation? Seems like the former after reading the foreword in the 2e rules.
D&D is the original game, published in 1974, and has a lot of differences with AD&D. AD&D was developed by Gary Gygax to have a more coherent approach to the rules in 1977. In D&D Basic, races were also classes unlike AD&D where classes and races were separate. The base mechanics of D&D Basic and AD&D are nearly identical with minor differences.
D&D Basic and AD&D became two separate product lines during TSR's ownership.
Zed Duke of Banville may be able to give you a more in depth explanation on the differences.
There were six editions of Dungeons & Dragons published by TSR, though it's important to keep in mind that all of these editions are closer to each other than to any new rules with the D&D name published after the demise of TSR in 1997.
1st: Original D&D, by Gary Gygax and Dave Arneson, consisting of the three "little brown booklets" (about 110 pages total) sold together starting in 1974, with three character classes (fighting-man, magic-user, and cleric). There were three rules supplements (about 190 pages total) --- Greyhawk (paladins and thieves, among many other new rules), Blackmoor (monks and assassins plus a sample adventure among other things), and Eldritch Wizardry (druids and psionics among other items) --- plus Supplement IV: Deities, Demigods, and Heroes, which was a precursor to Deities & Demigods / Legends & Lore but didn't really contain new rules.
2nd: Eric Holmes' "blue book" D&D in 1977 consisting of a single, 50-page booklet with rules only up to 3rd level. Not exactly a complete version of D&D in itself, but it sold quite well due to being cheap and comprehensible.
3rd: Advanced Dungeons & Dragons by Gary Gygax with three core rulebooks (about 500 pages total): the Monster Manual released in 1977, the Players Handbook in 1978, and the Dungeon Masters Guide in 1979. TSR began publishing adventure modules in 1978, about 100 specifically for this version of the rules. Two World of Greyhawk setting books by Gygax were released (the brief Folio in 1980 and the lengthier box set in 1983), although TSR only moved heavily into campaign setting material in 1987, after Gygax's ouster from TSR, starting with the Forgotten Realms box set and Dragonlance hardcover book. A few optional rulebooks were published beginning with Unearthed Arcana in 1985, not counting the earlier Fiend Folio and Monster Manual II with additional monsters or the Deities & Demigods / Legends & Lore book about representing (mostly) real-world mythologies with AD&D stats.
4th: Moldvay/Cook B/X D&D in 1981 consisting of the Basic Rules and Expert Rules (about 130 pages total), with covers by Erol Otus. The Basic Rules were a somewhat more expansive revision of Holmes D&D, while the Expert Rules took players up to level 14. Supposedly, this version of D&D had been intended to conclude with a third rules set that was never published.
5th: Mentzer BECMI D&D, published starting in 1983, ultimately consisting of five box sets (about 500 pages total) with covers by Larry Elmore. The 'Red Box' Basic Set was similar to Holmes and Moldvay Basic but much lengthier with a drastically revised presentation, and the 'Blue Box' Expert Set was similar to the Cook Expert Rules. The third 'Green Box' Companion Set took characters to level 25 and included rules for dominion rulership and mass warfare, among other things, while the fourth 'Black Box' Master Set took characters to the maximum 36th level with rules for questing for immortality. The final 'Gold Box' Immortals Set provided a new set of rules for playing as immortals that was almost divorced from normal D&D rules. Beginning in 1987, a series of Gazetteers were published detailing the various countries of the Known World, followed by a few campaign setting box sets and other material. A 1991 Rules Cyclopedia compiled the rules from the first four box sets, while a 1992 Wrath of the Immortals box set replaced the Gold Box rules for immortals with new ones. About 60 adventure modules were published for non-advanced D&D, overwhelmingly for the BECMI version.
6th: 2nd edition AD&D by David Zeb Cook, a revision of Gygax's AD&D, released in 1989 again as a set of three core rulebooks (about 600 pages total) but with the Monster Manual hardcover book replaced by a Monstrous Compendium contained in a binder. Most of the AD&D campaign setting material was published for 2nd edition AD&D, including everything for the new Spelljammer, Ravenloft, Dark Sun, Al Qadim, Planescape, and Birthright settings. There were also a voluminous amount of optional rules --- 15 Complete ____ Handbook's, 8 Dungeon Master's Guide Resources, 7 Historical Reference Books, and many more --- plus about 150 adventure modules and a considerable quantity of other material before TSR went bankrupt in 1997.