I've no experience here, but some gentle (& not so gentle) EQ-ing makes the listening experience quite a bit better here.
This link shows my settings for the 8 band eq from the calf plugins. No other processing done..

https://www.dropbox.com/s/8n7flw5ucz8741j/calf_eq_whiter_shade_of_pale.png

Toggling parametric III in the middle will take lots of the very highs out. Makes it feel "cleaner" to me, but I don't think
it suits this song, so I de-activated it. I'm sure you've done some EQing like this yourself with similar results.
I'm in the mood to play with some plugins though :) -H