Lancelot
Adventurer
That's why I'm not going to run B2. I love B2 -- it's in my top three classic D&D adventures of all time -- and I'd love to run it. But with only one game session for sure, it's a slow starter. If I were going to run a full campaign of BD&D, I'd start with B2.
B3 is a badly designed adventure module. I don't like it.
The B1-9 compilation, I just don't own. (I own B1, B2, B3, B4, and B9 individually.)
...ooh, ooh! I know the answer to this one!
Run B4 instead. I agree with your position on B2 (...needs more than 1 session to do it justice) and B3 (poorly designed; needs work). But surely we both agree that B4 is the Awesome Sauce?
Do Tiers 1-4. You don't even need to do Tier 5 (or anything below that). End the session with the raid on Zenobia/Alexander's tomb. If you've got bonus time, then Tier 5 can be a "stretch goal".
There are more tricks and traps than B1, some interesting NPC groups to interact with (or kill; last time I ran it, my group wiped out the Lawful/Good Brotherhood of Gorm by accident...), better dungeon design, and more thematic (e.g. the undead infested tier, vermin crawling through ruined rooms, dessicated corpses...). It's much more fun as a classic Basic module.
B5 (Horror on the Hill) isn't too bad either. I like it less than B2 or B4, but it has some classic encounters. For a one-shot, arguably, there is nothing more iconic than the situation that awaits on Level 3 of the dungeon...
However, if you're committed to running B1, I'd consider allocating bonus XP for completing quests or smart ideas, rather than simply upping the treasure count. Maybe someone wants them to map the dungeon, and will pay them 1,000 GP / XP for a map of each level. Or maybe they're looking for the magical stone on level 2, or the room of pools...