Warming up digital in my setup

If you have a tape loop, get a tube buffer. That should warm it up a bit. 

Definitely the phone setup.  Get a used Lumin u1 mini, Kimber Kable D60 spdif, used RME ADI2 dac fs. You will be happy. Quboz subscription. I use this setup in my den with PS Audio BHK signature pre and m700 monoblocks into Kef R11.  No glass.

I would definitely start with upgrading your source.

I started out feeding my dac with an iPhone, and it was terrible. I bought an Auralic Aries, and it was a night and day difference. My streaming (Tidal masters) SQ now beats the pants off red book CD audio fed into the same dac. Auralic’s Lightning DS app is incredibly easy to use. I love this unit.

There’s an Aries for sale on eBay right now for $599 which is a great deal.

Here’s a couple reviews of the Aries

If you’re feeding the DAC via USB, then the Laboga Emerald is significantly warm and "analogue" compared to any other I’ve tried.

A more expensive option is the Innuos Phoenix USB - this will bring benefits across the board, as well as taming the treble

I can immediately think of 3 tactics to get rid of the glare:

1. Get pretty much any competently designed R2R DAC--or better yet, a NOS (non-oversampling DAC). This will make a huge difference
2. Get a tube buffer to put in line after the DAC. My NOS DAC (MHDT Labs Orchid) has a built-in tube buffer circuit, which is extremely convenient. After rolling a few recommended tubes in that circuit, I kept the best new old stock tube and am very happy with the sound
3. And unless you're a big fan of MQA or DSD, invest in a good SPDIF converter + coax cable, enabling you to use coax, not USB straight into the new DAC. An upgrade to that is a DDC (digital-to-digital converter), which can also run a coax cable into the DAC.

I'm leaving out confusing details like I2S connections found on some DACs and DDCs.

Regardless--do at least 2 of those things and your entire relationship with digital will change for the better.