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

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.  

You're listening to music off of a Mac Mini. Invest in a dedicated streamer, that'll make more of an audible difference than fussing over DACs. Even a Wiim Pro with LPS (linear power supply) will beat the mac mini. A bit better, Limetree Bridge II or something, tiny German made machine and with an MCRU LPS it sounds like a much more expensive piece of gear. 

Then you can up your DAC game later. 

Contact Vladimir at Audio Mirror and see if you can snag a pre owned Toubadour III or IV that someone may have traded for the V. It will fit your budget and given you a great tune sound. He’s very responsive and can upgrade the components as well.

also +1 for the Okto DAC8 as the best inexpensive DAC around IMO.

You're listening to music off of a Mac Mini. Invest in a dedicated streamer, that'll make more of an audible difference than fussing over DACs. .....

Then you can up your DAC game later. 

Excellent advice. I'm sure there are thousands of people out there swapping DAC's every few months based on read reviews and making superfluous conclusions on the sound, then posting about it, without ever knowing the true sound quality. Sometimes people have to be made aware that having the cart in front of the horse just doesn't work very well. Take that same "harsh sounding DAC" put it behind a Grimm (for example) and "oh wow, not harsh anymore!"

You need to save up for a Wadax. That is the only chip-based DAC that sounds any good, 

You should write for Colbert.  

My suggestions:  Mac Mini USB to DAC probably isn't optimizing the SQ.  Some aspects are theoretical but before you go and spend any budget on DAC upgrades I think you want to get your digital source(s) in order:

• You don't mention the source material - Tidal? Qobuz? Stored FLAC?  Make sure you have some lossless material to use as a benchmark if for example you're listening to Spotify lossy.  Caring about the provenance of the source material, both in terms of masters and file formats, can be critical to maxing quality.  And this is probably something you can do without much up front investment. 
• Consider getting a streamer and connecting by ethernet to your mac mini as a streaming server. Software like Roon works well in that configuration, but there are others.  Streamers are just mini computers optimized for audio. You don't have to spend a lot to start - there are streamers that start at just a few hundred.  Just make sure to get one with compatible DAC connections for your gear.

This will create a baseline for you to listen, audition other DACs etc.  Don't just go and blow a ton of cash on a DAC upgrade (unless you really want a streamer/DAC combo), or if that's your plan at least get the foundation right so you can make good choices.

Also - just to throw this out there:  speakers/headphones are by far the most influential in sound quality.  Other things matter but doing that right is the best bang for the buck. 

2nd. the Audio Mirror Toubadour.IV...It uses the most expensive chip you can buy with tube front end. My system cost 35K and this $3,000 dac is all you will ever want. It makes music like non other under 6K. I've owned 2 R2R dacs and "thought" they were the most musical for the $$.....Until I put the Audio Mirror into my system...All I can say is wow...was I wrong !