This turned out pretty well. The photo looks more yellow than the actual stole on my monitor--yours may differ. It's really a good deal more gray than this. There are a lot of places where the brocade is quite worn, and several tiny splits in the silk. I have not tried to correct these for fear of doing more damage.
The next challenge was to deal with the deteriorating embroidered panels at the bottom of the stole. These consist of finely couched gold thread on a background of ribbed silk, a bit more coppery than the green brocade. In some places a horizontal band of the ribbed silk had completely worn away. I covered these with a thin bias strip of the iridescent silk. There were many loose gold threads, which I couched back down where they belonged. Unfortunately, some small areas of the ribbed silk have disappeared, revealing the white silk canvas interlining. They are too fragile to stitch over and too small to patch, so I have left them alone.
The embroidered areas are edged in what was once an elaborate green-gold braid which has darkened and stiffened greatly. I did nothing to this except to restitch some edges that had come loose. There are also a few areas of the ribbed silk which have turned black and stiff. Some of these are covered by the iridescent silk strips; one remains showing under the pineapple embroidery on the priest's left panel. Nothing can be done with this area as it's too stiff to stitch through and will fracture and crumble if bent very much. The silk fringe has blessedly survived pretty much intact.