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

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 !