Maybe consider the Sansa Clip+ or Zip :D. Very compact, easily carried player with expandability via microSD (64GB in mine). It has a good reputation for low output impedance (no loss in bass) and pretty decent power at lower impedance, unless you're trying to drive some headphones with 200+ohms of impedance. Plus many many other benefits too much to list here.
Most importantly, it's dirt cheap (~50USD) compared to other higher end players with similar audio specifications, easily being the best value for money player if you can live with its quirks.
Personally it's delivering pretty good sound through my CI/DTEC/WBFK combo at the moment.
Also to be sure, have you actually got a good sound with your laptop when using either of your DIY IEMs? I find it strange that there can be such a great difference just changing to the amp... My laptop has slightly greater bass than my Clip Zip, but nothing as muddy as you've described when changing sources/amps.