Did this 3 times last night with some friends.
#1 Timed out on the third level, no coins.
#2 Cleared third level with about 5 minutes remained and warped out, 400+ish coins.
#3 Cleared second level, didn't have much time left, so we warped out, 250ish coins.
The randomness makes it original each time, but you have to move fast.
The third time we were doing ok, but we ran into a NM frog that was a dominator, so he slowed us down.
After the "successful mission" the second time. We checked the Nyzel assault orders guy about saved floors. All of us but the one person that actually clicked the first lamp when we zoned in said "0 floor saved."
The clicker said his said "3 floors saved." But, then we tried to have him do the first lamp again, but he said the only option he had was to start on the 1st floor.
I've already read a few threads about some people that made it to the fifth floor in one run, but no one has said they were able to start on any floor but the first yet.
Anyone figure this out yet? If so, please share.
Our current theory is that either you have to do 5 floors in one run, or.... you can only teleport to the lowest level that anyone in the party has saved.