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OK  -  you've got problems right from the get-go.

you need a bi-filar secondary  for low leakage between the 2 sec wdgs  -    but just as importantly you need low leakage back to the pri side as well

your extant transformer does not provide this  -  hence lots of leakage L and ringing on the sec side  -  only solution right now  is lots of snubbing ( across fets ) for this setup  -  and we can't even see if the layout is any good  -  which may be adding to your woes.

Where are the V-ds  and  Vg-s  waveforms for this abomination on the sec side please  ?

If you have 500V fets on the sec side and you add just enough snubbing to keep the spikes to < 450V say ( at max Vin, 200V, and full power )   -  then the design " could "  work  -  albeit with a bit more EMI than you may have been hoping for,  as you have a CT  ( centre tapped )  Tx sec.

  -  the higher volts make the snubbers burn even more heat  -  esp if you are doing a crazy sw freq  -  which we don't know  (??)  -  100kHz ?

LOTS of current and high leakage inductance  -  and  possibly wiring inductance on the sec side  -  always spells trouble for newbies

We get transformers designed by a crowd called pwrtrnx ( in Chch NZ of all places ),  they are always just spot on  -   they demand all the power ckt information to arrive at a sweet design with detailed build sheets.

p.s.   -  any apparent double switching on the pri side you may see using this chip is due to too long dead times  -  sorting the dead times to match loading and Vin will be tricky for a newbie to set up  -  for leading and lagging legs are usually different.

p.p.s  designing snubber values is not trivial  -  many people initially use too large a C and not the right R value  -  there is an easy way to calc if you know the Tx leakage on the sec side  -  power is proportional to C size and volts^2  -  so it makes sense to get this just right.

[  worst case you could get a lot of 150V 5W zeners in a series-parallel combo across each fet,  3 in series gives 450V,  and say  3 sets in  //  gives 9 zeners overall on each fet  -  in free air they can do about  300mW each   =  2.7 watts   -  these will limit the peak V,  then the snubbers can add a little more to reduce ringing  -  you're welcome  ]  

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