No, I don't think you'd be dampening any of the benefits of your new lift by using trim packers. Sonoran Steel uses the 10mm trim packers on top of 890s for their system 7.2 lift which has been thoroughly tested and proven. I can't see the 906s reacting much differently.
I forgot that the measurements I gave earlier were with about 250 lbs. additional weight in the rear. I took all my crap out and the rear now sits at 39" exactly with the 891s and new 285s (250 lbs. only sagged my springs .25"). Seeing as though you're at 38.5" in the front and you were asking about the softer 890s, they should put you right there (38.5-39"). Here's a pic of mine for reference (with the 250 lbs. in the back):