Good morning Laurie and greetings from WAY up north!
The Beckstead family has gone through a lot of permutations in spelling.Many of them are likely the result of clerks who were semi-literate themselves and also from the name being "Anglicized" from the original German variations.Other variations I have seen include Beckstedt, Bechstedt and there was also one that I saw someplace (it's been a long, long time) with a "g" in it.
One of the fun, and albeit frustrating, things about genealogical research is learning how many "different" last names a family has.
Good luck on your search and remember, be creative with the spellings you are searching for, you might just get lucky.
Doug Beckstead Fairbanks, Alaska (Probably the Northernmost Beckstead in the world!)