I doubt the gun itself is bad. Usually when an entire color stopped working it was a bad cable or cracked solder joint, occasionally a fault in the video amplifier.
The muddy looking one describes classic symptoms of a worn out CRT, especially if turning dowm the brightness makes the picture sharper, or if high brightness causes streaking to the right. In my experience, Sony tubes respond poorly to attempts at rejuvenation.
I have a 14" Trinitron broadcast studio monitor that produces a phenomenal picture, it even does 1080p. I fished it out of an e-waste bin but I think they've cost around $10k when new.
The simple trick to pin down if loss of a colour is the tube, the tube socket board, or further afield, is to just swap the drive with one of the operating guns.
If the fault changes to another colour, the tube is not at fault.
The "muddy look" sounds ominous.
Another thing which happens with a dying tube, is
apparent "Luma/Chroma intermodulation", where the colour Hue changes with brightness ( I say "apparent", because, although it looks similar, one is a Composite video problem, & the other simply a display device failing)
Perhaps the more accurate name would be "Colour tracking".
Back in the day, you could get your tube "regunned".
This was almost always successful with Trinitrons, but less so with other tube types.
Sadly, along with the market for new tubes, that for regunning has died.