need advise, which is the weakest link in my audio chain

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Thanks. Nice photo. Yes, that looks like a challenging room. And the solution will be lots of dampening.
 

Are the big rectangular  objects in the corner bass traps? Your room looks perfect for tube traps. I would go to their site. You’ll see that three in front are used for a challenging room. Also carpet down to the speakers.

Also on the walls. I am not an expert by a long shot… but those do not look like they would be really effective. 

Yes the diffusion panels on the side walls leave a lot to be desired.
My recommendation still stands - absorption instead of diffusion on the side walls. Also, the corner bass traps up towards the ceiling…are they foam? They’re probably good at reducing echo but in my experience foam doesn’t do much for bass trapping and it tends to make the highs sound dry. 
I would start with removing the diffusors and placing absorbers there. Something like GIK 242 or 244 panels or something of similar quality and build including the materials used. 
This is a cheaper path forward. The more expensive approach is to replace your Bryston components with a good integrated amp. But the room issues will persist even with new and better amp. It will most likely be more tolerable. Again, DAC and cd player won’t get you there as quickly as the amp upgrade would.