I don't know for sure but I think you can connect the phone or iPad directly to the amp via USB. You may also be able to stream the phone through the Mac Mini.
I control my Mac Mini with a keyboard and mouse, hooked up through my TV so I can see what I'm doing. I don't use Roon or anything like that. Just straight from Apple Music, or Youtube when I'm listening to that. I don't know why a different streamer would make a difference in terms of tone, finesse, and musicality. That's really weird and the causes for why that might be happening have not even been close to reasonably explained but it may be happening with some setups.