Best way to soft start 3 transformers?

So I’m on plan for an amplifier that has 3 separate transformers (2x 150W, 1x 300W). Clearly I don’t want to press a power switch for all of those transformers without some sorts of soft start. The way the amp working requires the 300W transformer goes first and the after some seconds, the 2x 150W next. I plan to have a rocker switch at the front panel.

I wonder what’d the safest/most logical way to deal with the soft start and delay requirements?
 
...I don’t want to press a power switch for all of those transformers without some sorts of soft start....

A mere 600VA of core? (Not even real power at start-up)

I'm on the end of a long power wire and I bang-start a 5,000 Watt (starting) motor all day long. I remember bang-starting 300W-400W output (600+ VA cores) Bogen, Crown, PhaseLinear, and ABSystems power amps. The Bogen, out in a park on a generator.