SMPS + Bank Caps

Hi,

that behaviour is typical for most SMPS and the datasheet may tell You the maximum allowed capacitance value (typically quite small) for problem-free start-up. The inrush current triggers the current limit circuitry which often shows a foldback/trip&restart/hickup character.
The datasheet should inform you about the current limiting character.
You can find SMPS that allow to charge Caps .... just read them manuals 😉

jauu
Calvin
 
One of the major advantages of SMPS is not needing any large filter caps after it (and fairly modest ones inside it). Just 100uF on each rail for amp stability should be plenty on the output. But note you can't get away with pulling large transient currents from a SMPS, you have to respect its ratings.

I assume by 70k µF you mean 70mF? ie 70,000µF?

One approach to increasing transient load handling is to use a slow-start relay circuit on the filter caps so the power supply never has to provide large inrush currents.