What next?

Schiit Freya + (I use the original version) and maybe a Bifrost 2/64...both sound first class and are somewhat "el-cheapo a mundo."

You’re where I was 6 years ago, great speakers, crappy front end.  Buy a used Innuos Zen Mk3 and a decent DAC like a used Schiit Yggy.  They’ll make you happy!

As mentions by others herein, $2000 would make for a great improvement over use of a iphone with a purchase of a streamer/DAC. You will get a greater return on your investment in the amp and speakers.

If you can expand your price range a bit, an open box Bluesound Node N130 and a new or used Denifrips Aries 2 will make a huge improvement. You might also think about getting rid of Apple Music and going with Qobuz, Amazon Music HD or Tidal.

All the best.

Others have suggested, pick up a new or used Bluesound Node 130; used is about $350....not a Node 2i, there is only about a $30 difference at used prices; it is several years newer in technology.

Add a used Denafrips Pontus II DAC for about $1,300, or a Denafrips Ares II DAC for about $700.....but I'd strongly suggest stretching for the Pontus II if funds are available, it's a really really strong DAC for the money.