tn2106
First off, not all MOSFETs "like" to operate linear. You
should be sure these ones do. Is 5.5V less losses,
enough to drive the gate fully on and off? Are there
startup periods during which the cap network is pumping
and produces a weak, hence dissipative gate drive level?
Pay attention to startup simulations and see if you are
transitioning through, or to, someplace you don't want to
be.
Second, a degree of nonoverlap timing needs to be
built into the circuit. Shoot-through current, especially
with higher voltages, can shed a whole lot of energy
per cycle. There appears to be no thought given to
that in this design. Your '244 may not produce enough
break-before-make to allow the transistors to live.
To test this latter try breaking the totem-pole and substitute
a resistor load for the low side or high side, in turn, and
see if the smoke stays inside the case.