As a proponent of North American small businesses to just stop doing business with the EU my motivation doesn't stem from the ignorance of the system rather the knowledge if it: the fines will be issued by the relevant authorities of each and every EU state according to their own interpretation. Certain countries might see this as a neat little cash grab opportunity.
If Brexit has any impact (which is unlikely, but admittedly still unclear[1], [2]), incorporating again in Ireland or France is very easy and has similarly-minded regulators.
I just don't see the EU giving fines to American small businesses. What kind of money could they expect to get out of them? I'm curious though, what EU countries do you think are so desperate for money that they would basically extort American small businesses?