I'm glad you told this story, because it makes a lot of sense.
You're right about how the sequence used to happen. And honestly, I can't remember the last time I experienced more than maybe 30-seconds of the foyer. I have also experienced HM several times where the stretch room spiel was well underway by the time we got into the room.
Sometimes they'd open the exterior doors and usher people right into the stretch room, bypassing the foyer "scene" completely. And just like you said, we'd get out of the stretch room and still wait in line to board the doombuggies.
The staging was put in place for a reason, and everything in the foyer and stretch rooms are part of the show. For the record, most of these visits of mine were during the LOW season (early January, October).
Here's what we do to ensure the best show possible.
1. If you are not first in line at the doors.
Move up when they usher guests in but hang back at the last minute (act like you are waiting on a group farther back in the line) and this way you are positioned to be one of the first in when they get the next group.
*So as not to miss the first spiel
2. Upon entering, position yourself in front of the fireplace so you can make an easy entrance to either stretching room.
*So you don't miss anything while they herd everyone else in
3. EITHER - Position yourself nearer to the panel that will open to exit the stretching room *so you are farther up in the doom buggy queue, OR hang back and be the last out *so you catch the little bits at the end of the stretch and you aren't in a hurry (just hope you are far enough up in the queue before the next room dumps on you.)
#1 is the key to having a nice experience in my opinion.
As far as the 3 to a car, I have not seen that. I do remember when they used to load 2 to a car in Space Mountain and you sat in the other person's lap basically (whether you knew them or not.) When I was a kid I got good at timing my entrance so that I was near a group of eligible ladies. In retrospect I can't believe that system ever got off the drawing board.
I can only imagine how that brainstorming session at WED went:
John: Ok, so its a high-speed ride through space
Herb: Sounds good, tell me more
John: We'll have bobsled style short trains zipping through a dark building with stars projected all around, they won't know where they're going
Herb: Love it! What do you have for me on safety?
John: Sure, we'll have a little padded bench for them to sit on, the second person will sit between the legs of the first person, and we'll have a loose belt that goes in front of the second person, its really just for show.
Herb: Um, OK... So this bench, it doesn't separate the two riders, at all?
John: Nope!, if the second person isn't up in the first person's junk at the start of the ride, they will be by the end. Hard not to when you are zipping down hills and turns and don't know where you're going.
Herb: Ok, so we'll be keeping odd numbered parties together and having a lot of single riders right.
John: Oh no, that wouldn't work. We're planning on putting complete strangers together between each other's legs.
Herb: Wow...just...wow.