Stronger pull-ups will just assist the runt in rising faster since the lower resistance allows the data line capacitance to be charged faster. On the scope you'd see the shark-fin start getting taller as you reduce the resistance. Your logic analyzer is just showing the brief time that the runt was interpreted as a logic 1 by the logic analyzer. Data isn't clocked in until SCL goes from low to high.
I think what you are chasing there is a red herring. The Logic analyzer shows both data values being what they ought to be.
As you say though, I really think it's not the issue involved here. It's not occurring while clock is high so it's not messing with start|stop and it's gone before the next clock edge so it's not getting read as data.