EC/UL is more for like that it doesn't electrocute you or burn down your house easily. I don't think that has a lot to do with EM emissions but I might be wrong.
Considering all the flashing lights (pulses) and the constant energizing pulses to coils, it is no surprise that there are quite a few.
If your symptoms are caused from physical exposure or psychological in nature is for remedying at the machine level irrelevant, it is however relevant if you try to fix your sensitivity on your person, but that's a different question and not what you asked.
To get back to that, I don't know if you could do a whole lot other than trying to line the inside of the cabinet while trying not to short any circuits and set your house on fire in the process. That being said you still would get exposure from the top unless you also line the underside of the playfield somehow. I don't think that is really feasible though or may be impossible due to material thickness and composition needed.
That heaves you shielding yourself and the proverbial tin hat so to speak.
Either way, good luck and hope you can still enjoy the hobby.