I'm having trouble understanding why the mechanical limit of your newer derailleur is less than your old Acera. Check over the Deore derailleur to make sure there are no physical defects (ie foreign debris, limit screw, etc).
Have you followed Park Tool or other guides for positioning the height of the derailleur?
As for "compatibility" issues, I was merely implying that the Deore should still shift to all three chainrings. I believe its targeted towards 9-speed applications (should be 8-speed compatible), but you're using and IG chain which I believe is a bit wider than the 9-speed super narrow HG chains.
Have you tried adjusting the derailleur rotation? I seem to recall reading either in the Park Blue Book or Shimano's documentation that you may need to rotate the derailleur slightly off parallel for proper shifting.
Switching from a Chinhaur 111 to a Shimano 110 may not actually get you 1 mm. Not all brands of square taper are 100% equal (ie I had problems putting a TruVativ crank on a Shimano bottom bracket). Granted, a Shimano crank on a Shimano BB should be the "correct" matchup, but the Chinhaur 111 may account for the difference.
You can try reinstalling the bottom bracket. Remove it, clean the threads, regrease, and replace. Torque the drive side first for alignment, then the non-drive side. You'll need to remove the cranks for this and for measuring your bottom bracket. A crank puller would make it easy, but not impossible without one.
At this point, it starting to sound like a trip to the bike shop though. It's beyond me...