Nobody knows all details about all figs cultivars about possible more than a few hundreds out there,but in my experience ,yes you got a Col de Dame White ,a healthy variant right there in the pixes above.
It matches ,the black and grise I have to a tee,so how can I say otherwise.
Good for you you hit the Jackpot.
Now slowly cuttings from this specimen should be grown all over the south,and replace Celeste,because it is way superior to anything grown in the south now except other Col de Dame,in fact all color of this cultivar are superior to anything else and about equal to Madeira figs,tho not identical.
Edit note:It would be nice ,that in order to convince us ,even better that you hit the Jack pot,to post pixies of the mature mother trees,that way we all will put to rest doubts,as to the existence of these old trees.
Otherwise someone might think you propagated new trees from meristem of the old diseased trees,and ,out of the lab,the young plants are fig mosaic free.
And if the second situation is a fact,it is your business but it would be nice to know.
Here is a pix of my Col de Dame Grise 5 years old plant.
Can you show us your tree?