Question: Would replacing the SR with either a Transparent G5 Reference or G6 Ultra make a noticeable difference in the sound?
Likely Yes, no guarantees.
Or other suggestions?
You have a very well balanced system. Upgrading PCs would likely be positively noticeable, but low of diminishing returns it may not be worth it. Maybe try/borrow a higher quality PC to try on each component. Otherwise, the change would have to be your choice - changing the speakers or electronics.
Another option is to add vinyl. I have both.