I am late to the game but will give my MHO in responding to your 3 questions:
1: Why do I prefer R2R based DACs to chip based DACs? - as I have posted before it is not the processor technology but the execution of the designers intent that matters. Some of the most respected and costly DACs use chip or proprietary processor technology (Chord, Solution, Bricasti, Mola Mola, Wadex). Generalizing, and it’s dangerous to do so but I will, R2R DACs produce a detailed but soft presentation while chip based and proprietary DACs produce an equally or more detailed presentation that is upfront and forward. If you audition products like the Bricasti M1 S2 or Mola Mola Tambaqui and compare them to the Denafrips Terminator 12th or DCS Bartok the subtle difference supporting the generalization is evident. This is a subjective hobby and it’s good you are using your ears. Many prefer the softer presentation. I don’t and shy towards chip based products.
2: Am I spending enough? SQ generally improves with price to a point of limiting return where increased price is not proportional to improved SQ. IMHO that point for DACs is around $5k. DACs in the $5 - $10k range the will perform better but return on improved SQ less proportional, and more similar than different to each other. Difference become a personal preference and are driven by the designers intent. Two rules apply to spend. First, spend must be correlated to the rest of the system. You would not realize the true potential of a high resolution $20k DAC in a $3k system. In fact, SQ may be worse than a lower resolution DAC due to component mismatch. Do not underestimate the significance of system matching. Second, spend must to correlated to your budget and acceptance of your significant other, the latter to avoid the pains of purgatory to amend. Only you can answer this question.
3: What is my next improvement or upgrade? You seem to be happy to a degree with your current DAC. You state you are still using a PC as your streamer/server. IMHO I think you would realize significant improvement with a dedicated streamer/server. There will be a significant reduction in digital glare, more black background, improved detail , and imaging and staging. Contenders would be a pre-owned Lumin U1, Innous Zen Mini, or Aurender N-100H all coming in at around $1k … and get a good digital cable of your choice that mates with your DAC. Another possible totally different direction offering an across the board improvement would be power conditioning. Good SQ starts with good power. I found significant improvements in my system SQ with improvements in power conditioning.
Good luck. Others in this thread gave you solid recommendations for R2R DACs in your budget if you stay that course.