I am answering my own question with information I have gathered after doing some of my own research. Several hand mills claim to make peanut butter, but the mill that seems to have the best public following and reviews for flour making, the Country Living Grain Mill, does not claim to make peanut butter in their marketing literature. I contacted the manufacturer, and got this reply:
We do not recommend doing nut butters in our mill. However, we are applying for patents on a nut butter attachment for the Country Living Mill that does a superlative job.. We hope to have it available by this Fall.
We have noticed that other grain mills on the market claim nut grinding ability and even show butter coming out of their mills. We have purchased these mills and tested them and quickly realized that it was an arduous task at best to produce anything resembling nut butter...we can do the same with out mill but feel that it is misleading and certainly unfair to make such claims. Hope this helps.
Of course their answer has every reason to be biased, and not tell me if there is a good peanut butter hand press available on the market.
Another popular press, the Wondermill Junior Deluxe claims to make creamy peanut butter with their stainless steel burrs, and one Amazon review agreed it was possible, but too messy to be worth the effort.
Reviews of two different griners at http://www.grainmillcomparison.com/ seem to agree with the general consensus that hand-made peanut butter isn't the state of the art (yet):
The nuts wouldn't feed, so I had to mash them into tiny bits. At this point the bits began to feed into the grinding plates. Unfortunately, those bits never exited--even when I loosened the grinding plates. The only peanut butter that I managed to produce was the goo stuck between the plates. -- GrainMaker Review
My test with peanuts resulted in the grinding plates clogging almost immediately, and I produced only a few flecks of peanut butter during the five minutes of grinding. Many companies claim their handmills will grind nutbutters and oily seeds, but I've yet to see one that wasn't a miserable failure in actuality. -- Wondermill Junior Review
I have not been able to find a single first-hand account of making peanut butter with a hand mill that said it was worth it. As already mentioned, the amazon review mentioned above said it was far too messy. Many other reviews I've found have said the end result only vaguely resembled peanut butter--and never creamy peanut butter.
In an effort to directly answer the question at hand, though, the only feature I so far have been able to find that is required specifically for peanut butter is that the mill have steel burrs, as opposed to stone which are desirable for finely ground flour, as the stone will absorb oil from nuts, causing the system to clog.
EDIT: I got an additional reply from the Country Living Grain Mill manufacturers, explaining (in no great detail) what is required for a nut-grinder:
There are a number of factors such as the mill must reduce the nuts to a manageable size prior to grinding, and propel them with enough pressure to be squeezed out between appropriately designed grinding plates. It sounds simple, but the reality is that it's a very tricky thing to manage.