I have been contacting Dr. Barinov and here's the E-mail I was sent recently:
Hello Dan,
The package price for LON surgery is 14 500 euros for a month's stay in hospital. Now we practice mostly LON alongside with Ilizarov. Lengthening by 6-7 cm (2-2.5") takes about 3 months and each extra month costs 1 000 including accommodation, meals and medical care. After lengthening is over, the frames are taken off and the person can go home. The nails are usually removed about a year after the surgery when the bones fully heal.
If the price suits you, I can tell you what documents you need to apply for a visa.
What are people's experiences with this doctor, I've been having trouble finding too many diaries.