What do you need to design a pulse transformer?
Peak voltage and current, pulse width, required rise time, repetition rate, the droop you can accept across the flat top, and the load. The volt-second product sets the core, the droop sets the magnetising inductance, and the rise time sets how hard we have to fight leakage and distributed capacitance.
Why does the rise time depend on the winding, not just the core?
Because the edge is limited by leakage inductance and by distributed capacitance, both of which come from how the winding is arranged rather than from the core. Interleaving reduces leakage but increases capacitance. Which one to favour depends on your source impedance and your load.
Can you build a single unit?
Yes. There is no minimum order quantity. Research and pulsed power work is very often one, and the same drawing scales later if the machine gets replicated.
Do you handle high voltage standoff and partial discharge?
Yes. Encapsulation, creepage and the insulation system are designed for the standoff, and partial discharge is tested and reported rather than assumed from a hipot pass.
Can you work from a schematic rather than a drawing?
Yes, and for pulsed work that is usually the better starting point. Send the circuit and the pulse you need at the load, and the first proposal comes back with estimated losses, the inductances and the expected hotspot temperature.