Inductor kickback snubbing with capacitor
No, there's nothing you can do within reason other than add a voltage regulator or make R3 extremely small and maybe C1 even bigger. The kickback represents stored energy in the inductor and it has to drive that energy somewhere when the switch opens. In driving that energy somewhere, it inevitably produces a voltage greater than the quiescent voltage.
When you added the series resistor, the spike is still there but woven into the waveform and you have a mixture of regular switching and back emf that when combined are hard to distinguish from each other.