This all happened by accident, and while goofing around while I waited for the other randos to activate the portal in the center of the final boss room.
You need to bring your sparrow into the boss room. However, this normally can't be done due to players being forced off their sparrows once you reach the stairs leading into the final boss room.
However, there is a way to get a sparrow in there regardless. I think it has something to do with where players are positioned in the boss room, because the last time I was in the dungeon as of this post, one of the other players was speeding through everything with their sword and hover board to skip rainbow road asap.
By the time they entered the boss room, I was on my sparrow riding up the lift pad, even got the countdown timer for pulling me through, but I made it to the top before it reached zero, so I didn't lose my sparrow.
Then I drove past the point where you normally auto dismount your sparrow, but that didn't happen, and I was allowed to bring it into the boss room.
Once the encounter started, I just started driving around the outside edge where the three bosses were to keep the sparrow intact until the portal opened up. It should be noted at this point I was using the new combat sparrow at the time.
But when I drove my sparrow into the teleport pad with the other players, a few things of interest happened.
First, my teammates got sent down into the DPS area, while I was stuck in the teleport pad while I was still riding my sparrow. I did jump off it after a moment or two, but I wasn't sinking down as normal, because my sparrow was now stuck beneath me, and I could flip it endlessly.
Second, while I was unable to see what was happening down in the boss room, I was able to figure out what my discovery had done by looking at the boss health bar. Their immunity shield was still active, and all the time I was stuck with my sparrow beneath me, my allies were unable to do any damage to the boss.
And third, after experimenting with this new discovery, assuming of course I am the first person to figure all this out anyway, I was able to blow up my sparrow so I could sink into the teleport pad. Except I wasn't being sent down into the DPS room where my allies were still waiting for me.
But after swinging my sword around a few times when only my head was above ground, I was able to get underneath the teleport pad, and there seems to be some space to crawl around underneath there. I didn't explore it fully, because I didn't want to hold the others up longer than I had already done and ruin their run for them.
So I managed to jump back up into the teleport pad and found a lot of taken psions waiting to kill me. Which thankfully set my spawn point inside the DPS room and allowed us to proceed as if nothing went wrong. And all future teleports were glitch free as well.
Hopefully this discovery will be of use to the community somehow, even if it's mostly just a fun thing to do from time to time.
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After a bit of testing on a few more runs in Prophecy, I think I've found a way to ensure you'll be able to bring your sparrow into the final boss room. Assuming everyone waits for the sparrow driver at the lift pad at the end of the rainbow road, and once the sparrow rider has ridden their sparrow up into the pyramid, have the driver wait at the bottom of the set of stairs right after being lifted inside. Then, have another player kill all the taken thrall and enter the boss room. Once the objective marker on the left side of the screen has fully updated, the sparrow driver can ride into the boss room without having to worry about auto dismounting. Just make sure you don't start the encounter until after the driver has entered the boss room, otherwise the stairs will close on them, and the only way they'll be able to enter is by killing themselves. So far I have not tested what will happen if two players enter with sparrows, but I don't think all three players can do it, since anyone entering the boss room will auto dismount and their sparrows will respawn once they do.