Ha! I've seen this. We had one screw that was close enough to a trace on the board that it would lock up the device and fail ESD testing. Ended up plugging the top of that one screw hole with RTV on the whole batch.
Precompliance EMI test is cheaper than ever to put together, but a proper ESD setup is still going to be impossible to justify on a shoestring. I’ve seen other people use leak detectors and record zappers and I won’t even get into the things that won’t credibly work. I feel your pain.