Sounds like a serious problem.
If there was enough debris accumulated in the filter element to trigger the deltaP sensor, then you have a serious issue. I'm sure your engine lube circuit also has magnetic chip detectors, but if they have not given an indication, then the debris source is non-magnetic and is not due to a gear or bearing failure. Chip detectors typically have a filter screen around them, so your mechanic should pull both the chip detectors and their filter screens to check for debris.
Since the cooler is downstream of the filter, and you apparently have cooler contamination due to contaminated oil being bypassed around the clogged filter element, then you also will have contamination of your engine's bearing oil jets and bearing chambers as well as your entire EMAD lube system. So the entire engine should be taken out of service, torn down, and inspected. Not just the oil heat exchanger and EMAD.
I've seen all types of non-magnetic debris end up in turbine engine lube systems and EMADs. Most of it originates at manufacture and assembly, and is sometimes composed of harmless substances like rag fluff, or other times more damaging debris such as core sand, machining chips or grinding wheel fragments. If this is EMAD debris, it circulates around in the EMAD lube system until enough collects on the filter to trigger the deltaP sensor. Or as in your case, it clogs the filter enough to pop the bypass valve.
Turbine engine lube systems are designed with enough filters and safeguards to prevent any catastrophic failures. That's why you're still around to ask this question.
Good luck.
riff_raff