I'm using Eagle H-beam rods and have never had any problems at 600 Horsepower and I'm sure Mike and some of his customers are making a lot more horsepower and more rpm's. I'm crossing the line at 6700 to 6800 rpms and the engine is built to go 7500 and I think I exceeded that recently when I broke the drive shaft and hit the reve limiter
As far as DOVE vs Edelbrock heads I can't give you any advice on the Edelbrocks although I have heard good things as well as bad, mostly bad things about the assembled heads. I'm running DOVE CCJ heads and they work wonderfully!! Either way you go you will need to have the heads smoothed out at a minimum, remove all the rough castings. Buy them bare and have a good machinist mildly or wildly port them, your choice, as well as assemble the heads with all of the matched components from the cam of your choice. I prefer solids over hydraulics myself and would actually be running a Roller if I could have afforded the extra expense at the time.
BTW I wouldn't install 2.19/1.72 valves in the heads if you're going to run them on a 390. Valve shrouding becomes an issue and you won't be dissapointed with the 2.09/1.66 valve sizes with your combination.
Good luck