I have not, but I also haven't found my go-to IEMs (JHAudio JH13Pro) particularly unfriendly, as far as loads go. They are pretty low impedance but also stupendously sensitive. I am of course prone to a confirmation bias here, because I want to need nothing other than the DAP itself. My primary uses for the AK240 are: 1) travel: train commutes or flights for work/pleasure 2) digital source when I don't feel like lugging a laptop around. I would like to say that I'm being critical in terms of the sound quality in the first case, but I'm pretty sure I'd stick with it even if it did need more muscle. In terms of specifics there, in any event, I don't find a lack of power with the JH13s, I could easily blow my ears. There are other aspects of control, but I don't think the player is lacking punch, control, etc. Frequency response seems (not surprisingly) pretty darn flat/neutral (it has an EQ, I haven't used it).
I haven't tried some of the other high-end DAPs so I'm basically stating this in a vacuum (versus a ton of portable DAC/AMP/iPod configurations I've used in the past): I think the AK240 probably delivers about the best sound I would expect in a small all-in-one does-everything box. Beating it would probably require certain changes. A discrete class-A high-power output stage that was still quiet would be one option that would be interesting, but I don't think it's needed for the species of IEM I've tried. It would also require a lot more surface area to evacuate heat and a giant battery, negating the form factor. And, it's not like the battery is particularly generous as-is, already. I would generally not want to use the AK240 directly with headphones not designed to be driven by consumer equipment: I think it's fine with sensitive cans like the Oppo PM-1 or NAD HP50. While I have not yet tried it, I don't think I would directly use it with something like Audeze, Sennheiser HD6/7/8xx, AKG K7xx, etc.
That said I did finally audition the various DAPs and DAC/Amps I had wanted to although using a SE connection in all cases with devices which provided balanced out options. I agree that AK had the very best sound, I was astounded by the quality of the DAC and the impact it had on the music - increased clarity, separation and very quiet background (I guess the amp's contribution on that last one). Strangely enough while I felt the drums in "Rolling in the deep" didnt quite have the thump on the AK, the drums in a "Hotel California" (live recording) FLAC sounded superb, reminding me of a listening session of the same song on SACD on a friend's musical fidelity monoblocks driving Norrh 9 speakers (one my very best listening experiences ever) many years ago. Conclusion of course that low end on a good recording can yet carry muscle on the AK. Loudness was never the challenge as you pointed out. I tested exclusively with the Roxannes. Also the UI was smooth and intuitive. The DAP that came close on SQ (better amp but less capable DAC) was the HiFiMan 901 with better low end punch but laggy UI and larger form factor. What was a surprise however was that at less than half the price, the Theorem 720 had a rivaling DAC and amp losing out only in size/weight and of course the need for a source. Maybe the AK120II is a good compromise, with identical sound to my ears and losing native DSD capability. Thanks a lot for your comments. 
