Ugh...I have had a couple of lots like that over the years
You can try magic eraser on them as their will be a surface coating on there but I have only had a limited success with this. Enough to notice a difference but not enough to get the colour back. Unfortunately although you have mentioned you do not wish to sun fade - after you get the coating of yuckiness off you will be left with stained plastic and the sun is the best option.
I am not a fan of oxy in most situations but in this case its not as though you are going to make them worse, so I would certainly be giving it a try. You can put the head in the oxy - just make sure not to put the hair in. I use a string over a container and hang the pony by her hair up to her hair line.