Perhaps a pair of used pair of Campfire Audio Andromedas. They seems to be a jack of all trades universal IEM. They retail new for $1100 USD so I'm sure you could find a good used pair for under a grand.

Neutral: Audio-GD's NFB-11.28 ($330) Warm: Schiit Valhalla 2 ($349) or Bottlehead Crack ($299)

I don't believe Fidelio X2's require the amount of power to warrant purchasing an amplifier.

Quite possibly the greatest April Fools joke to have ever come true. Congrats to the Schiit team.

Portable on-ear open-back design... I wonder who would be the target customer for these headphones. Perhaps Audeze made a good choice to make the Sine DX a limited run.

I suspect the V20 is your best "audiophile smartphone." But, be warned, the V30 may be right around the corner...

HD800S is definitely a solid choice. I agree with Sheldaze's choices as he seems to have the most experience with these headphones. However, I would definitely suggest testing gear if you have a local audio store or any meets coming up in your area.

Audio-GD's NFB-11.28 is a solid option for a Chinese DAC/Amp under $500. As long as you're okay with only single-ended output, the device has a lot to offer for a package that starts at $330.

USB cable or toslink optical I would assume.

How long will the special go on for? If you have the time, I would suggest demoing them in your local area if possible.

HD-650s by far. If you decide to upgrade your gear, HD-650s will upgrade with it.

I would suggest saving up for a more meaningful upgrade as well. HD-600 series headphones can really shine with the proper amplifier.

The m50x doesn't need any additional power from an external amplifier. Perhaps a quality DAC could work well with your setup.

I would suggest lossless versions of a wide variety of music. It is important to understand all strengths and weaknesses of the DAC you're testing.

I would suggest m40x. In my opinion, they are certainly a fair choice in the price range. They honestly beat out the m50x. People tend to pad swap them so that is always an option if necessary.