Component size check - Using SSR on PS_ON

[OwenD]

I'm re-arranging my system somewhat and decided to split my power supplies and use PS_ON.
The three power supplies will be
1: Meanwell RS-25-5 (5v 5A) (only for standby power)
2: Meanwell 480-24 (Main power to Duet for motors etc)
3: Meanwell 120-12 (Powers water pump and some fans)

SSR in use is a 40amp DC/AC unit. Datasheet here

I have been using this SSR on the 500w mains powered bed for some years and was thinking of using the same model to switch on/off the 12v and 24v power supplies via the PS_ON pin.
They are easy to obtain and have a very large heat sink available

I'm relatively confident on how to wire it all up, but my main concern is whether the SSR can handle (long term) the inrush current of the two power supplies.
The datasheet for the SSR says it has a maximum surge current of 440A (20ms)

Both the 12v & 24v supplies have an inrush of 35A.
Logic says that means a combined 70A if I control both from a single SSR.
But is that exceeding the specs of the SSR in question?
I can source the same SSR in 80A and 100A sizes, but have to order them in and price is double what I can get the 40A unit locally.

In the grand scheme and extra $40-50 is nothing for what is after all supposed to be a safety function, but I'd like to get a better understanding of how these should be rated.

I have considered using a mechanical relay, but finding a suitable unit with a 5v coil is difficult.

Wiring diagram

[o_lampe]

@owend
In our electric cars, we had inverters with huge capacitors. The solution was a pre-charge relay, which (in your case) slowly charges the input caps of the PSUs before it gets passed by the SSR. Not sure if this could be done by only one PS_ON pin, but what is live without challenges