The only two R2R DACs that I've owned are the MHDT Orchid (in stock form, no mods) and the Aqua La Voce S3. The Orchid might be the most "analog" sounding DAC I've owned, very easy to listen to, perhaps just a little on the "warm" side.
I give huge props to MHDT Labs and Jiun. I bought mine second hand and the USB input wasn't working. I contacted MHDT Labs about getting it fixed, being very up front about the fact that I wasn't the original owner and that it wasn't under warranty. Jiun sent me a new board free of charge.
The La Voce S3 provides a lot more detail and dynamics, without sounding "digital". It seems very true to the music, however you want to interpret that. I have owned a number of other DACs and the La Voce S3 is the best I've had to this point. It's out of your budget new, but TMR has an open box one for under $4K. If you're patient, you might find a used one within your budget.