No, what you say matches others' characterization of the Grado 1000i. All Grados are light in bass (strongest one is the RS1, the classic one with a wood button on each earpiece center), and the GS1000i in particular has hot treble. I love that...gives me a transparent "you are there" feeling, but others have found it too much.
The GS1000e, like all of the Grado e line, softens that treble, increases the bass, and gives 3dB more sound for a given driving power. While that sounds tempting, to me the GS1000e also has a distracting resonance in the bass, only noticeable on comparison with other Grados, as if the bass is coming through a barrel that tends to emphasize one frequency. It is one of my least favorite Grados!
I think your DAP is plenty strong AND has a good DAC. I don't think you are limited by that.