I'm not familiar with SoundCloud, I note they say that the streaming is all encoded at 128k mp3, which won't help matters ... but that it's possible for the uploader to set the track to be downloadable for a visitor, at full quality. Is this something you could do?
Repeated recording loops via speaker will certainly compound, Tom Danley of Danley Loudspeakers notes that 3 rounds are usually enough.
I differ on the impact of generations of DAC/ADC, I actually tried some of the samples put up here, and it does degrade, similar to numbers of generations of tape - in particular, the transient sparkle is slightly dulled. If one didn't have the two to compare then it would be unnoticeable, and obviously since many commercial recordings are derived from a generational tape well down from the master it's not that severe a problem - only if they're side by side will the closer to the original be distinguishable.