I had 2 Oscars with one JD and the oscars beat the crap out of the JD he would never some out of hiding. It all depends on the fish. a JD and and O could get along great or not.
The EBJD is a bit more shy and weak. Mine is not a fighter but he rules the tank. I keep mine with a severum they get along great. I think the Oscar could be too much for the EBJD to deal with.
I want to clean something up. Not all EBJD get parasites or health problems they are no harder to care for them the normal. The only thing is at 2" the weak ones die off. If your 2" EBJD grows and does well then you got a healthy one and will be the same health wise as the normal. they are inbred thats why many die off at 2".