I think the Head Box II is neutral. Imho it is absolutely right in this regard.
I think that it is a bit rolled off in the highest frequencies but at that price I think that would be normal.
It is not "warm" and personally I am very pleased about this.
So, if you can get a chance to listen to the Head Box II then of course you should.
However I do have an additional comment.
I don't know anything about the Beyerdynamic DT880-32 but I've just done an Internet search and I see they are quite expensive.
You write that they are "dry" and analytical, well I have never heard them, but my experience of very good transducers used with mediocre amplification is that the result is very often "dry" and "analytical".
I think that it might well be that simply getting a much better amplifier which is giving the Beyerdynamic headphones the levels of detail they would like might cure this "dry" and "analytical" thing.
Very often at head-fi I see people using very expensive headphones with mediocre amplifiers, but this will not work well.
They report a "dry" and "analytical" sound and so they buy a warm sounding amplifier ending up with what I think is something worse than what they had before, now they have low detail covered up with a euphonic soup.
I think that rather than go down this "warm amp" thing, it is very much better just to get an amplifier which is actually very good. By that I mean one that will give the Beyerdynamics the detail I suspect they would love to have.
The best way to get a good amp on a budget is second-hand.
I tend to steer away from amps that are described as "warm", "lifelike", "organic" etc.
Get an amplifier which honestly increases the amplitude of its input without effects 
Good pure class A solid state amps are very well worth looking at. Musical Fidelity is one company that has produced these at an affordable level but there are many others.