Cuk converter implementation
LTSPICE works just fine for simulating the normal Cuk topology, I can't see any reason why it wouldn't work here. Just make sure you model the parasitics appropriately, the same as for any SPICE simulation.

I've personally used the LM5022 (with normal FETs) for standard Cuk, I can't see any obvious reason why it would not work on this topology either. The main switches just need a complementary waveform, so a simple inverter should suffice, and the synchronous rectifier pair will be simple too. 

There are some nice single-chip high/low side drivers like the IR25604 which might help too.