Help understanding/selecting SMPS to drive capacitive load
You've identified the problem fairly accurately, for capacitative load the instantaneous current requirements are quite large. 

In many designs short circuit detection simply disconnects a load when a short is detected reconnecting it when the short is gone . In this case your capacitor does not ever fully charge before the short circuit detection triggers, causing the saw tooth waveform you observe. 



SMPS Vendors often include a variety of features, namely


soft-start
inrush limiting (snubber)
short circuit protection. 


Sometimes these features may interact with each other.

Soft-start and inrush limiting are intended to mitigate the startup characteristics of a capacitative load. 

Short circuit detection protects the supply due to accidental short and typically attempts to restart the supply as soon as the short is removed. But it has negative performance implications during a large inrush on start. 

For example, a larger than expected inrush may trigger the short circuit detection, which turns the supply off. As the current load drops the short circuit detect unlatches ...  restarting the supply to the same inrush. Rinse and repeat to give you the sawtooth waveform you observe.



General Suggestions


Identify the in-rush current specifications of the supply, these are typically 10x more nominally than the rated supply current. Understand how this relates to your your measured in-rush load.
Identify the nature of the soft-start circuits and inrush limiting on the "working" supplies, the slow supply startup may compensate for larger than expected in-rush.
Use external soft-start or in-rush snubber to avoid slamming the full capacitance load on startup and be agnostic to the features of your upstream SMPS. In a pinch this can simply be a small value series resistor to limit the inrush current, say 100Oohm in series with the capacitor, which is disconnected from the circuit when it is charged.  



  Note: It is hard to say if the worse performing supply is actually a "worse" product, in principle you are simply exceeding its specification, if the supplies are nominally the same specification and you are exceeding both of them, it is probable that the one that allows the large in-rush will function but fail prematurely. Or it may have a slower soft-start and does not trigger the short circuit detection, meaning it is a better design for your purposes.