1. Where in the US did they immigrate to? Immigrants tended to go where others from the same village went, so sometimes researching those folks yields clues. I'm assuming Texas, based on a google search of the name, but an exact town would help.
2. Frank's tombstone: Nar = born (narodil abbreviated) , Listopadu = of November, Zem = died (zemřel abbreviated), Unora = of February. The remaining words are a prayer, similar to "Grant him eternal rest, O Lord." Not significant genealogy-wise. There is no guarantee that 20 Nov 1854 given to you is his birth, because sometimes it was wrong on their baptismal certificate issued when they immigrated, so that's what they went by. But it is probably close. The style of the prayer is quite Catholic.
3. Does anyone have a baptismal certificate or any other documents with Czech writing on them?
4. We have a Hrnčir family in my home county in Kansas, but they arrived after the 1890s. And they phoneticized their spelling, Hrnchir. Agnes Smajstria's origins might not provide a clue to Frank's, as once they got here, the custom of marrying someone from around your village diminished.
Mary Sramek Levesque