The primary needs to be centre tapped and fed at that point via a commutation choke.
The choke only smooths out the changeover pulses, when both devices are on.
With two separate chokes, the current in each will be trying to vary as the transistors switch and being stabilised by the choke at the same time, so fighting each other.
Personally, I think those so-called ZVS circuits are rather nasty; they do not switch cleanly and can fail to oscillate, blowing the power devices.
A separate feedback winding with suitable bias would be far better.