Welcome to the forum!
I was in you shoes about a year and a half ago. Bought a 6.0 (after two 7.3L), had lots of issues, (EGR and oil cooler related) but once the kinks were worked out, not an issue since.
If your EGR is sticking open due to getting fouled up, you could be in the early stages of an EGR cooler failure. Exhaust soot coming through the cooler, mixing with a tiny coolant leak, and gunking up the EGR valve. You'll also want to check for white chalky matter around the coolant degas cap.
This is actually a chain of faults, starting with the oil cooler.
Simple explanation, oil cooler stops flowing coolant, and in turn deprives the EGR cooler or adequate coolant for cooling, so the hot exhaust gases generate excessive heat within the EGR cooler and damage/crack the EGR cooler. Replacing the EGR cooler will not permanently fix the problem, you must
also address the oil cooler. There are several options to consider, but first I would start immediately by monitoring the delta between you Engine Oil Temps (EOT) and your Engine Coolant Temps (ECT). A higher EOT than ECT indicates an issue, and a delta of 15° to 25° indicates a significantly blocked Engine Oil Cooler. You should do this while driving on the highway, level ground, steady speed for 15 to 20 minutes.
You can do this monitoring with an Edge Insight CS or CTS, or a ScanGaugeII (cheaper option)
This is a highly recommended MO for any 6.0 owner, even those with a completely stock vehicle.
FYI, I have a ScanGaugeII, EGR Delete, External Oil Cooler (OEM cooler delete) from BulletProofDiesel (BPD), and mild tuning and exhaust. 150k on the clicker, no issues, OEM head bolts/gaskets, truck runs away from my 7.3L's all day long.
ERIC - Tennessee Powerstrokes Chapter Director
2011 K1500 Silverado Z71 5.3L Vortec
2004 F250 Super Crew FX4 Powerstroke
1997 F250 Super Cab 4x4 Powerstroke
2004 K1500 Silverado Z71 5.3L Vortec
1999 F250 Super Crew 2WD Powerstroke ZF6
1998 K2500 Silverado 5.7L Vortec