Ah, I was thinking of mentioning another alternative, but I did not because of the complexity. However, since you stated that you are actually ripping your BD/DVD discs onto computer files and then playing them, there is another option. (ripping is usually too complex a process for most people).
You can look at one of the high end media players, such as Zapitti, Zidoo or Dune. You would just take your ripped movies and copy them to a SSD which can be inserted into these media players. These will likely have better video quality than your computer.
The Zappiti Reference actually has a built-in DAC uses ESS saber dac chips and full linear power supplies for everything:
https://www.zappiti.us.com/product-page/zappiti-reference
It's way over your stated budget, but it's an all-in-one box. The DAC may actually have more resolution and detail than your ifi (it's difficult to tell).
Another option with high-end power supplies and dac is Dune Ultra 4K:
https://www.dune-hd.com/collections/frontpage/products/dune-hd-ultra-vision-4k
Dune has a lesser model with smaller linear power supply and uses AKM dac instead of ESS, but it's only $699:
https://www.dune-hd.com/collections/frontpage/products/dune-hd-max-vision-4k
If you want to try one of these media players as a digital coax transport only, the cheapest way to go is a Zidoo Z10pro:
Then add a good external linear power supply for this such as Farad Super3 (or Keces if you have a budget, or even a cheap china ebay Teradak).