That said, the only consideration I would address is whether a source that can "go loud enough" is actually driving its load correctly. I have used my 200s with my Galaxy S3, and while it certainly plays loudly enough, on average, I can hear it clipping trying to drive 96dB/16ohms. For comparison, the GR07s are 105dB/50 ohm, and the MH1Cs I couldn't find any specs. I also have SM3s and ASG1.2s, which are in the over-100dB club, and are much easier to drive and are better matches for lots of portables.
Many of the 'issues' eke seems to have with the JVCs seem related to drive capabilities. I listen to my 100s (I have both 100s and 200s) amped by my Centrance dacmini fed from a sonos via coax digital (it's my couch system. I hear none of the issues you bring up, but i also listen primarily to acoustic jazz.I also want to point out that i am not a spec-head, but think that impedence and sensitivity are extremely important specs to look at when matching, so to speak, an amp with a pair of speakers, i.e., dap to iems.