Bel Canto DAC 1.1 at under $600 will substantially improve the sound of that player - this is just one possibility. The above cost estimates for DACs to improve on the Music Hall don't match my experiences with that unit. I wouldn't expect most used DACs in the $400 or below range to do you much good, however - but a notch or two above that ($500-$750 even), you'll find several models that can substantially improve on its sound.
The CI in particular I would not worry about - you'd notice differences, but not all of them "better"... it's a nice unit, but very entry-level. I've owned it as well and would not recommend it to improve on your player.
Keep in mind, just because a DAC may have similar "hardware" (DAC chips etc.) as your player, its likely that its analog output stage is built to a higher standard as a standalone unit, and will be packing a better power supply etc. These differences can produce substantial performance gains.
The Music-Hall is a "giant-killer" to some degree, but I find that in their enthusiasm for the product, people can overstate that accolade. A decent mid-priced DAC can certainly help this unit achieve better performance.
The CI in particular I would not worry about - you'd notice differences, but not all of them "better"... it's a nice unit, but very entry-level. I've owned it as well and would not recommend it to improve on your player.
Keep in mind, just because a DAC may have similar "hardware" (DAC chips etc.) as your player, its likely that its analog output stage is built to a higher standard as a standalone unit, and will be packing a better power supply etc. These differences can produce substantial performance gains.
The Music-Hall is a "giant-killer" to some degree, but I find that in their enthusiasm for the product, people can overstate that accolade. A decent mid-priced DAC can certainly help this unit achieve better performance.