I could just slam on the square wave drives and let the TI chip current limit until the caps charge up. That might work.
I was thiking I could start the two half-bridges with in-phase square waves and then slowly slide them out to 180 degrees. My FPGA kids could do that. That would be a nuisance to Spice.
We did a similar supply a while back with discrete fets, no current limits. Startup made 300 amp spikes that made all sorts of problems.