Ah, the heat & humidity plus chores kept me away for a while, but on with the show!
The circuit above I drafted this morning, as a modification to the one posted previously. It allows the standard row-scanning on-PCB circuit to be adapted to impulse operation.
R1's value is chosen to drain C such that the voltage drop across Z keeps it in the breakdown region for the desired operation time. When the voltage across Z falls to breakdown, Z becomes nonconducting. The high-value (megohm) resistor R2 then pulls the base of TFT2 down, shutting it off and extinguishing OLED.
The circuit does not, at OLED, generate the ideal square-wave source. It does, however, suffice to provide sufficient impulsivity without the requirement for more transistors.
Transistor budget is at most three on mass-produced glass-photolith'd planes, due to defects. Even the single transistor behind LCD LCs is frequently defective, causing 'stuck' pixels. This is one reason why the previous design, while an excellent demonstration of good technique, will not be feasible in a mass-production scenario.
This circuit is a crude first approximation of something which can do the job. There are undoubtedly other implementations which perform better and stay within a three-transistor budget.