The solder mask on a pcb is mainly for aesthetic reasons as well as protecting the copper and allowing the use of flow soldering for production. Whilst it does have dielectric properties, I doubt it would make any difference in your application.

As for the suggestion of conductive coating the enclosure adding cost - if the machine doesn't work it is worthless! One has to be careful where we save cents - it could cause a more expensive problem later on. I dare say your requirement of fixing the problem without adding any cost to the product is expecting the intervention of the Almighty. There is no Father Christmas either. Sorry!

Whilst I'm being philosophical - most people tend to blame anything they don't understand whilst overlooking the most obvious problems. I had the instance where an electrician was blaming my light dimmers for being faulty when the real problem was a blown light bulb. Same site, there was a number of 'faulty' earth leakage circuit breakers - the problem was a leaking fountain. Moral - always look for the obvious.