To answer OP's question, that kind of has already happened. Baam would have, more than likely, defeated clown-face ranker that he was fighting prior to Kallavan.
As far as notoriety? That's sort of already happened as well. The new chapters hint that his deeds at least facing Kalavan and other high rankers and living are getting passed around the grapevine so to say. Without spoiling too much. This is to be expected as that is a huge occurrence. Facing Kallavan and living is arguably more interesting than merely defeating any old ranker.
I also agree we don't have the literal time. Think about how long this series has run in real time, and then think we're only at floor 50. Now almost triple that amount of time to reach the upper floors and have the resolution. SIU could make this series go on forever if he gets into upper floor breakthroughs, thousands of years in the future or past, other towers, axis interactions, etc - but just this one ascension is taking forever.
Baam should be regularly on par with newly ranked rankers by now (if not handily defeating them). There is still enough of a gap from low-tier rankers to high rankers that we'd have plenty of good material to go. We should be well past regulars. Regulars can't hold their weight against data Zahard, or last 5 seconds against Kallavan.
Then, as pointed out, there is the war. Big players and groups have started to move. That will soon take over the run-of-the-mill tower-climbing story. We're going to have to get some bigger skips than we have since Season 3 started. Imagine if real nations took years to go to actual war after a war declaration - this is seemingly too slow-moving. At least IMO.
Even after the milestone floors there is plenty of room to go after Baam gets to the top. The story can continue with the first assault on Zahard failing, and regrouping. There are PLENTY of factions and pro-Zahard high-rankers in the same vein as Kalavan to contend with. There are even bigger things at play than Zahard even (tower government, the workshop, ancient ones' motivations, administrators' motivations, higher floors to go, axis powers, etc).
So the story doesn't have to conclude at 135 by far. Really, that is where it could really take off considering all the pieces in play. There are billions of residents and tens of thousands of rankers. I think we'd be OK if Baam was at least halfway up, or more, and fighting on par with rankers already!