I tried some experiments using phase control on the SSR to slowly turn off the transformer over 50 cycles (1 second), followed by a test using a few whole cycles starting at a zero crossing.
I noticed there was still some increased current surge (2 times normal on the first half cycle), depending on the polarity of the first half cycle of power. Apparently, the demagnetizing wasn't complete. However, it is a lot better than starting with the core fully magnetized in a unfavorable direction. Results may vary with transformer type.
You may also be able to put the core in a consistent magnetized state after a test, and always start at opposite phase.