How would I go about calculating the time a constant current source takes to recover from a short?
To the extent possible, I’d look for graphs of “load regulation” in the datasheet, which graphically depict the regulator’s response to a load change. But that seems like maybe an uncommon thing for LED drivers (neither of the two parts we’ve been discussing have those in their datasheets).
Alternatively, if the regulator lists its control bandwidth in the datasheet, you could use the old rule of thumb to relate that to the rise time. For instance, if you’re modulating at 38 kHz, and you want to be sure your rise time is less than 10% of a period, you’d want it to be less than 1/380,000 = 2.6 microseconds. From the article, you’d want a control bandwidth of no less than 0.35/2.6 microseconds = 133 kHz. (or you could just say you want a bandwidth at least 3.5x your carrier frequency).
Using that metric, the MAX16834 is more than capable - yet despite that, the datasheet suggests (not a hard spec) that PWM dimming is functional only up to 20 kHz. I don’t know how to explain that discrepancy. This is where I’d buy an eval kit and try it out to see what I’m missing.