Pulse transformers and V.dt ratings
Am I correct in calculating the observed V.us as 190 


No, you're not, I think.
For simplicity, let's consider 'worst case' with 50% duty cycle (in fact it is not worst, all duty cycle are equivalent, but let me not go to such details at the moment).

First, transformer coil (because of C4 Cap) gets only AC component, so it magnetizes from -V.us to +V.us which effectively doubles available span.

Second, at 50% duty cycle C4 charged to the half of the driver supply (i.e. to 5V DC). So, primary winding gets only 5V amplitude).

Third, saturation should be prevented only while half of the clock period, because while the other half transformer magnetizes to the opposite polarity.

Hence transformer should have 0.5*5V*10us=25 (not 200) V.us  product to avoid saturation. Datasheet states for Minimum V.us, so concrete sample may have  value, greater than 15.

So, those are reasons, which in my opinion may explain why you find it works well at 53kHz.