It depends also on what ESD standard you are required to meet and also the permitted disturbance - 'Needs power cycle to recover', 'operational disturbance but recovers without intervention' , 'no disturbance in operation' etc.
Putting a ground flood on the top side may help but I doubt that tented vias would resist most esd tests. You can certainly use supply rail clamps, esd protectors on critical signals etc. but I think it's probably virtually impossible to design a (electronic) circuit with zero susceptible nodes.
Putting the active stuff and nodes on the underside of the PCB would help of course, but beware of clearances needed against a probe applied at the edge of the PCB.
A cover is clearly not your preferred solution but it might turn out to be the safest and even possibly the cheapest solution too.
Another key issue on anything Din rail mounted - presumably on a plastic base, is how good your protective ground connection is, relative to its I/Os.