Summit County was not in existence until 1861. So, I wonder if the County will have any records of before then? Maybe, but a lot of the early county records have been turned over to the Colorado State Archives in Denver. There is a Summit County Historical Society, there might be some help there.
You are talking about very early state history here. The records might not have recorded as you might think of in the East.
I did a quick check in the Historical newspapers 1859-1861 and came away with no hits for Ehpraim/Joshua Bartlett.