Timing rattle is fairly normal on these trucks, it has to do with timing, cam, piston design, etc... Reman injectors can also be a bit noisier than others.
It can be tuned out, but it can also be made worse with tuning. If I run a stock tune on my truck is quite noise even with my BBI's, but I'm also running 03-04 pistons. My current UDC Pro tune is dead quiet and as quiet as any 5.9 I've heard run.
The 06-07's aren't more tuning challenged, in fact they have more tuning options as EFI works on them when it doesn't on 03-05. There are some distinct differences from 04.5-05 to 06-07 but the guts of the tuning is the same.
For box tuners I prefer Smarty and for custom tuning I also prefer Smarty with UDC Pro. UDC Pro offers more tables to adjust than EFI Live and Smarty on deals with Dodge/Ram Cummins where EFI primarily deals with other platforms.
I wouldn't put an Edge on anything.