I can second Paul's assertion that the S.E.X. Amp might be a bit too noisy. It might be down to the quality (or lack thereof) of my build, but mine works best with stuff that's harder to drive. My HE1000V2 sound fine because they are low sensitivity (35 ohm but only 90dB), my Sennheisers and Audio-Technica sound fine because they're high impedance (97dB and 300ohm, 98dB and 470ohm), and my AKG K240 sound fine because they're a thirsty combination of low sensitivity and high impedance (600ohm 91dB). Those things lower the noise floor to the point it's quiet.
My Grados (32ohm 99.8dB) and Focals (50ohm 104dB) are a little bit noisey with no music, and they're both less sensitive than your Meze 109s (40ohm and 112dB). I don't think the S.E.X. is a good choice for them. At 112dB your headphones are basically noise detectors.
EDIT: By noisy, I mean in a quiet room with no music playing through the headphones there's a very slight background hum that is in no way loud enough to interfere with music once it's playing. With your headphones it might be a bit more than slight.