The EGR will not dump fuel into the engine oil. A failed EGR will put coolant into the engine, I believe. Before you waste any more money do an oil sample this is a very low cost tech solution to identify what is in your oil. Geno's Garage sells an oil sampling kit for $26.00 a unit. Or you can go to Blackstone labs for a kit that cost $28.00 a unit. The report back will provide information on percent of fuel dilution, soot and water by volume in the oil and other contaminants in the oil. This will provide information to you and your mechanic as to what is wrong with your engine.
I do a sample every time I have changed the oil since new I have over 16 sample reports.