It is questionable. Why is everyone waiting for Zahard lol?
Eh I thought that high-rankers were constantly taking the guardian test for the 135th floor? That's why Zahard (+10 families) recruit them right? It's just that no one passes the test for some reason...
*Cough.
Only Irregulars can take the tests from the Guardians, Thats is why the original inhabitances of the tower never climbed it (since Irregulars comes from OUTSIDE THE TOWER (not Outer Tower)), but then Zahard made some kind of deal with Headon, what this deal contains exactly we dont know but it can be concluded that it allows "Normal" citizens of the tower to climb the tower "if" they get choosen by Headon.
So only an Irregular can "climb" the tower (the Regulars hitches a ride on the back), and Zahard stoped for some reason on the 134th floor, so in order to go higher then that a Regular have to team up with an Irregular that takes the next test, But the Irregulars are following:
Phantaminum - If he even exists, he has only been sighted once in the Palace of Zahard, since then and before no one (as far as we know) have ever encountered him, so he/she (if exists) is probably from a Higher floor already.
Enryuu - Little is known about Enryuu in terms of locations and relations, but as far as we know he/she doesn't have a known location and he/she doesnt seem to be a team player.
Urek Mazino - The most active one of the Irregulars, and even have an establiced faction, but his goal is to exit the tower and not climb it.
Zahard - Has an establiced faction (his empire), but is currently inactive, and you can join his "forces".
So Zahard is the only option for the regulars that wants to go up.
It might even be so (higly plausible) that the ranking system was establiced so that they would compete in order to rise in ranks, for the very purpose of being of allowing them to improve themself to their limits so that Zahard can take the strongest with him when he resumes his climbing.
The value of Irregulars (I think) supports the idea that Viole truly is a part of FUG, since in the two competing factions are both lead by irregulars (they have an irregular on their side), I believe that FUG can't hope to compete openly against the Zahard faction without the backing of an Irregular and since Urek has completly different goals, Zahard of obvious reasons and the other two (we cant be sure but can only guess) cant be contancted nor wokr with others, this means that in order to even beging to topple Zahard FUG needs an Irregular, therefore all the work put into getting Baam into the tower matches up with the importance of getting him to join.