"so, the real question is whether there is a CD player for less than $2k that sounds better than the 105D?"
Insert the word "new" in front of "CD player" and the answer may well be "no" or "not in any audibly significant way".
It seems that the 105D is right at the sweet spot of that price range re: price/performance/versatility and must have a really good digital section as Dan Wright stated that, "Oppo’s stock clock “is excellent and unique,” and its DAC (employing two ESS Sabre ES9018 chips) “is exceptional.” He added that because they could not improve upon the clock or the DAC, Modwright left them alone."
http://www.theabsolutesound.com/articles/modwright-oppo-bdp-105-with-truth-modifications/ Exemplar also chose the 105 as the model to modify for their latest and only current digital offering.
Dan chose the Marantz SA-8005 for his latest Truth mod, possibly due to Oppo discontinuing the 105/105D. Seems that the 105D and the SA-8005 are the current kings of the latest <$2k players until the new models are introduced...
Dave