Transformer humm and SSR?

The SSR probably uses a triac as switching element that will switch on once the voltage across the terminals has reached a certain voltage (I'd guess around 10-30V). This provides the voltage needed to operate the SSR circuitry on the switching side. And it also cuts off the first few percent of every sine (half)wave which leads to a current spike through the trafo at triac turn on time. From my POV there's little to nothing you can do about that except use a mechanical relay.
 
Yes, the ones I have use traics and I started looking for mosfet SSR's but they seemed harder to find and more expensive.

I am building a soft start as well and consider using the triac ssr for the NTC soft start and then shorting the SSR/mains feed with a mechanical relay.

This should bypass the triac issue (even though there may be a bit of humming at the start). Not sure though if the SSR will be "unhappy" being shorted?