Why do I prefer R2R over Chip based DAC's?

The DACs you are looking at flavor one thing over another.  A true R2R DAC does not always sound better or more musical then a Chip designed DAC, that comes down to parts and design.  For your budget of $1000 you would be better off upgrading the DAC you like now with key parts.

Happy Listening.

Just look for a Holo Audio May and your journey will end. 

R2R has nothing to do with your OP.

@grinell why get a used MHDT when you can get a new Orchid for roughly $1,200 (what I spent a couple years ago)? I highly recommend it. Excellent DAC with a tube output stage.

R to R is the most overrated format ever it has horrible stats, if you put different forms of Dolby to get the his down you have to align and figure out what type of Dolby to decode. Only about 85 db of dynamic rage with all the many ratings they came up with to make that number less embarrassing. R to R never fooled anyone what I mean is when we played back the R to R the people in the studio or control room always knew you were playing back, when digital came in it fooled many people into thinking the musician or actor was really playing or singing live it startled many people, that was a real and honest reaction. 

Tape is a little like records it sounds great because of the warm distortion and hum during the music, yes it sounds great and the distortion of tape saturation is perfect and emulated everyday in digital form, but no don't think it's good it's not.