Any Improvement Possible for B&O-Hsu-Paradigm-Apple System?

That sounds like a highly-reflective and huge listening space.  I'd invest in some sort of room treatments to improve the experience.  It may take several different types to not only improve the sound, but also to not make the room look like a recording studio.  The right rug(s), decorative acoustic panels, diffusers, etc.

Yes our room is a combined living/dining/kitchen with lots of glass.  There is a carpeted stairway into the space, and 6 tall thin bookshelves along the walls.  I’m going to start room treatments today with more utility rugs at the speakers.

if you're committed to your speakers, a dac would be a logical upgrade--in your range i'd look at chord or smsl, though there's many others. room treatments are always a good idea as well.

I thought about a new DAC. In my research I found this article - https://www.kenrockwell.com/apple/airport-express-audio-quality-2014.htm

Ken’s beginning summary of the Model A1392 states, “Good: Fantastic audio quality, full 2 V RMS output, beautiful, sturdy build and small. Bad: Much clumsier to set up the first time than Bluetooth.”

Then he shows about 20 pages of graphs and charts, none of which I understand. But there are frequent comments throughout such as, “perfect…marvelous.”

Ken concludes, “At any price the Apple AirPort Express is a great DAC. It sounds great, with a completely silent background, full 2 V output, smooth detailed sound and full infrasonic bass response.”

My AirPort Express is set up and running well. I think I need to upgrade the weak link of my system to gain any improvement. Is that my DAC? Or is the quality of the internet radio I’m using as the source the limiting factor here.

I agree that the room has a lot of hard surfaces which cause mid range glare and screechy highs. However streaming from the I pad leaves a lot of room for improvement. The room issues can be dealt with by strategically  moving the system  so it does not have to fill up a whole space. This does not mean that it won't be heard. it means that a dedicated place can have the best sound and spill over to the remainder.  A preamp / Dac may be the best route. You would still stream from the Ipad but it would run to the preamp / dac. The preamp & dac will make for better sound. After that, get a dedicated streamer. The ipad is without a doubt, the weakest link. The room has good possibilities. That's why I would not be concerned with that now, especially with the budget you have

I assume you have curtains on the windows. Closing them will make for less brightness & glare. You may not notice the glare now due to low volume. but I am sure you will notice it if you turn the music volume up

Yes, I only need the best sound in one place.  I don’t need to try to achieve more than that.  There are no curtains, so soft surfaces are just a sofa and the carpeted stairs.  Also I only need to achieve the best sound at about 20-25% of the sound level bar on my iPad.  That would cover about 98% of my listening.

Thx for all the suggestions!  I didn’t find an smsl DAC on the buy/sell posts, and the cheapest non-portable chord was $1700.  So I think I’ll look for a minidsp shd.