Do you know if the shuttling can work in the opposite direction?
My mom has early onset osteoporosis due to a decades long problem with her parathyroid. A recent surgery fixed the parathyroid with amazing results but she is now in the slow process of recalcifying her bones. I wonder if the K vitamins you mentioned could help speed it up.
Vitamin K2-MK4 in particular, and MK-7 rather less so, causes excess calcium in the blood stream to be put into bones, where all excess calcium should go, if not be excreted.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4566462/
Do consider the need for magnesium, Vitamin D, and boron when making bone.
https://www.healthline.com/health/managing-osteoporosis/supplements-and-vitamins-you-should-consider