Just use the single device in circuit, not 2 in series. The sidac will turn on and start to heat the cathodes, and then at every zero crossing will turn off, and once the cathodes are hot they will start the tube conducting, which clamps the voltage across the tube to around 90V, so the sidac will then stay off till the tube is turned off long enough for the heaters to get cold.
The electronic starters use a bridge rectifier to make DC, then a simple thyristor to short the tube when power is applied, with a sidac or series diacs to get the thyristor to trigger at around 140VDC across the pins. Then there is a second circuit, consisting of a high value resistor fed from the bridge rectifier, which charges a capacitor up to turn on a transistor, via a low leakage high voltage zener diode, that shorts out the gate of the thyristor, so it will not fire. This is there for EOL of the tube, so it will attempt to heat the cathodes for around 30 seconds, then shut down and refuse to try to heat the tube at EOL, so it stays off, and does not keep trying to flicker and start. Other types use a triac, and a single diode to rectify the incoming voltage to drive the sidac and sense circuit, same principles.