I think you're on the right track of sending the CD output to a high quality DAC. Consider Jay's Audio CD + DAC. Very musical and engaging.
My current DAC is the Rockna Wavedream Signature, which you should be able to find for around $5K if you're open to pre-owned. It has a lot of inputs and could take the USB or SPDIF signal from the Schiit piece. The Rockna is very lively and dynamic and will provide excellent detail.
I also have the Wavedream NET server, which has a nice CD transport. It only does Redbook CDs though. I have a small collection of SACDs and wanted to be able to enjoy those.
I still have an Oppo 203 that I rarely use. I purchased an HDMI to i2s converter and used the HDMI out on the Oppo to connect to the Rockna DAC. The Rockna has 2 i2s inputs, and I can use the Oppo as a transport into the Rockna DAC. That combination was a huge improvement on the DAC in the Oppo.
As far as R2R versus other types of DACs, at the end of the day it all depends on the implementation. Having said that, I like the idea of FPGA which allows upgrades over time. I have a MHDT Labs Orchid, which is a very "analog" sounding DAC and easy to listen to, but I don't think it would provide the type of listening experience you're looking for.