Hey guys, sorry for not giving you an update in some time.
So here it goes: I did try setting the out to +4dB, and that improved the end result A LOT, truly. However, I can't really say the issue is solved. I still felt like some of the "roar" in the distortion was missing. I did try recording other dry signals, through DI box or not, with input set to -10dB and to +4dB, and I didn't find the "perfect" reamping setup, really.
The best setup I found was recording the dry signal through the DI box (no attenuation) in the input at -10dB and reamping through an output at +4dB, to the reamp box and then to the amp input.
But then again, the closest, yet not quite the same. I don't know if you guys have any further suggestions... (however, I won't be able to try any of them for some two weeks now, being away from home in this time)
