The little dot mk.iii has three adjustment settings for various impedance headphones, however I didn't get good results with my he560's. However my matrix m-stage drives them very well. I've yet to try earphones.
Ok, I'm not familiar with the LD mkiii but usually OTL amps has a pretty high output impedance.
The A2's 16Ohms/120dB and really easy to drive, that's probably why I feel that the m-stage is overkill for them.
Tbh as long as you guys are happy that's all that matters, I was just surprised (and had a different experience pairing them with the m-stage ).