Bob's advice is good, and might be an argument for using Internal Volume:
http://wiki.jriver.com/index.php/Volume#Internal_Volume_Headroom
However, I'm struggling a little to understand how this is a DAC issue.
If a DAC is always smoothing the digital input, it's going to be introducing distortion (over-extending any sharp change) and should appear if its specs are measured.
Why would this distortion be any more relevant at full amplitude than half amplitude?
Sometimes the answer is yes, sometimes no. Let's start with first principle: There are many devices and processes which produce greater amplitude on their output than on their input, including: filters, equalizers, sample rate converters, oversamplers, and lossy coders. Severe distortion and strong high frequency equalization in the source material produces even greater intersample peak output on a proportional basis. More "normal" material only goes over the sample peak occasionally on the output of a DAC. I have a simplified explanation as to why this occurs on page 70 of the second edition of my book, "Mastering Audio". Thanks to B.J. Buchalter for that revealing diagram.
Anyway, let's look at two cases and see if it answers your question.
a) You can have a recording made in a pristine fashion, without severe processing, material whose sample peak reaches up to 0 dBFS on a sample measurement, which will go OVER 0 dBFS and cause distortion on the output of the DAC, simply because of the upsampler in the DAC. This will overload the DAC and produce additional distortion that was not in the material. Simply turning down the digital level in front of the DAC fixes this problem and the sound can be pristine again.
b) You can have a recording which was highly processed and which is inherently distorted (e.g. name the latest pop release), which produces even higher intersample peaks in the DAC. Turn it down digitally and you fix the additional distortion which the DAC had added, but it still doesn't get rid of the distortion due to the extreme processing, it still sounds bad.
How's that?
From the mastering side it makes sense to avoid flat-lines at peak amplitude in the digital signal simply because natural sounds don't have flat peaks. A digital flat line at the top of a wave will sound bad with any DAC or speakers. It seems like a DAC that over-extends could actually even sound a little better in this case if the over-extension acted to "naturalize" the unnatural digital flat line.
I think this is a misunderstanding. "Over-extends" is actually distortion, it overloads the output of the DAC. See
http://www.tcelectronic.com/tech-library/mastering/ and read the article: "Stop Counting Samples" and the article "0 dBFS+ Levels in Digital Mastering", and "Programmed for Distortion" by my friends Thomas Lund and Soren Nielsen.