I just saw your message of a year ago on this family. My Greenslit grandparents lived about 16 mi. south of Roundup 1917-1924. I have a short family history of sorts written by my aunt when she was in her 80s. She was 9 years old in 1918. Here is an excerpt:

"In June 1918 some neighbor children Martha and Nicky BUDAVENITS (her spelling) came to play with us, and they said they were going to start summer school at the Pinedale School, 3 1/2 miles east of us and wanted me to go, too.".. "The teacher's name was Miss Nelson." etc.

In June 1918, the Greenslit family lived on 'the Folsom place', which my aunt described as being about 16 mi. south of Roundup and then 1 1/2 mi. off of the main road which ran from Roundup to Billings (this would be Hwy 87 per my atlas).
I live in Calif. and have never been to the Roundup area.

I'm wondering if her "Nicky Budavenits" is your Nick Badovinatz. What do you think?
-- Helen Greenslit Graves