I think I'm sloowwly understanding how everything is supposed to work.
From the sample schematic (far bottom right where the transducer is):
https://www.electro-tech-online.com/custompdfs/2007/11/650020module20spec.pdf
It seems that the transformer is working more like a flyback inductor (with the transformer step-up) to provide the high voltage drive, rather than operating like a normal step-up transformer as I originally thought.
THe PDF also mentions that at the end of the 16 pulses that are transmitted, a 200VDC bias remains on the transducer for the receive operation. Is C5 just there to stop the transformer's primary from draining away the charge (and killing the DC bias) that's in the capacitance of the transducer during the listening phase?
It seems that might be easier on the transformer, as far as initially charging up C1 in kchriste's DC bias circuit goes.
EDIT: On second thought, maybe C5 acts as a DC-bias storage capacitor (rather than a DC-blocking capacitor to retain the DC-bias charge on the transducer capacitance). DUring the listening phase the primary side of the transformer is open circuited so the secondary would appear as a small series combination of winding resistance + winding inductance (appearing as a DC short) which are in parallel with the capacitance of the transducer plates?
EDIT2: I think the thought in my first edit is wrong since the polarity of the charge on C5 and the transducer places aren't charging each other, they are facing the same way the capacitors discharge through the seconary winding resistace of the transformer- which leaves me at a loss as to how the circuit is able to retain the DC bias on the transducer capacitance for long enough since it just gets leeched away by the transformer secondary winding resistance. C5 also seems to form a capacitive divide with the transducer capacitance so I have no idea how it works anymore.