I Inductive heating and eddy currents

[MagneticMagic]

You need to look at the energy put in over time.

I did exactly that.
dB/dt * time = some J

Look at B in cos function
There are 4 distinct quadrants (that last gify shows it)
0-90deg (Bmax to zero)
90-180 (zero to Bmax)
180-270 (Bmax to zero)
270-360 (zero to Bmax)

The zero point is where dB/dt is max, as shown in that last gify.

I evaluated only the 0-90deg in my math above.
0-90 has a dB/dt, or J value from eddy (in my example, J per 25usec)
The overall J in eddy per full one cycle of frequency is the 0-90 J * 4

The push-pull in DC is technically AC.

To get same Bmax you need 100A DC, or 70.7A AC_RMS

My math should be correct.