The big problem with just using a logic gate output to switch timing on a 555 via the resistors is that when the resistor is pulled LOW, it makes timing difficult to calculate.
So use a diode in series with the extra resistor. Or use a PNP transistor as a high side switch, better because of the very low saturated VCE if designed/selected well.
R1 + R2 controls the ON time, the time that determines the servo position.
R2 merely controls the OFF time. It should be longer than the ON time, so we’ll use a diode to make it so only R1 controls ON time.
Put a diode in parallel with R2, cathode to pins 2 and 6 (triangle pointing down in the schematic above).
Now OFF time is about 0.7R2C1, and ON time is 0.7R1C1 (slightly longer because of the diode drop).
Then connect a diode, cathode to an incoming digital signal, anode to a resistor we’ll call R3, the other end of the resistor to the junction of R1, pin7, and R2. Now when the input signal is HIGH, R3 is placed in parallel with R1 so ON time is (slightly more than) equal to 0.7(R1//R3)C1. Where // means “in parallel with”.
Now you just need to figure out if the pulse must be longer or shorter for the servo positions you need, then calculate and adjust R1 and R3 accordingly. As a start, servo mid position is about 1.5ms, with 1ms and 2ms being the limits of travel (roughly, depending on the servo).
For time between pulses, OFF time 0.7R2C1, I’d go with about 10ms.
You could also do this by altering the voltage at pin 5, but that gets a bit more difficult, math-wise.