The oiling system is not an issue with a 390 or 428. Lots of 390's and 428's in Super Stock NHRA turning over 8000 rpm. My own 390 dyno mule made many pulls at 7500 with a hydraulic roller cam... Like anything else, you just have to know the "fixes". Even a 427 S/O won't live at higher rpm without different things being addressed.
People seem to really underestimate what a 390 will do. They will *easily* make over 500 hp with the correct combination and will do it in a way that you can drive it on the street/highway all day long.
I built a 390 a few years ago with a hydraulic roller camshaft, Trick Flow heads, Performer RPM intake, and 10:1 compression. It made 540 hp on the dyno here and powers this '66 Galaxie station wagon. The owner drives it everywhere and drag races it when there's an event to go to.
My 445's with TFS heads make 540-550 hp and 590 lb-ft of torque. That's also with a 390 block.