The general rule for cutting trees back, whether they're neglected fruit trees, ornamentals, perennials which used to be shrubs and are now a...bit
... larger, is:
==> Do not remove more than 1/3 of the tree during any one year. <==
If you need to cut the trees back by 1/2--and I worked with a fig one time that was completely out of hand--trim them back 1/3 this year and 1/3 next year. I can't tell you what the consequences will be of cutting the trunk/main leader back will be; figs aren't a single-leader kind of tree unless the owner keeps on them constantly. Even then, for the sake of easy harvesting of the figs, multiple laterals make things much easier.
What happens if one breaks this "rule"? Trees/plants can go into shock and become much more susceptible to disease, insects, drought, whatever Mother Nature may be sending their way in any case. Since these trees have great sentimental value, I strongly suggest no more than 1/3 and possibly even only 1/4, as the previous member recommended, this year, and the same next year, based on your close observation of how they do this year.
Hope it works out well.
Sunset Zone 17, USDA Zone 9