Travis,
A few hints. First, I wouldn't worry about the "Johann". Most people had several first name and only one was the name they were called by ("Rufname") and other than in the US (i think) there was no rule if this was the first 2nd or 3rd name. "Johann" was a VERY common name, at time >50% of male boys had that in their collection of first names and the parents would rather pick one the more distinguishing names as Rufname. I have that very often in my list of ancestors.
You can write a mail to the archive in Hannover and ask if there more pieces of information in the document or ask for a copy of the doc. It would cost a fee though and need some patience.
You will easily find Kleinenborstel when googling it or look it up on google maps. It is now part of Martfeld and lcose to Bruchhausen. The website of Martfeld has some info on families and their history. "Meyer" is listed but that was a very common name. "Zimmermann" is not but your ancestor is called a "Häusling" in the record, which means he did not own land and was just living for a rent on one of the farms. Zimmermann is not an uncommon name in Germany but not so popular in Lower Saxony.
Regards,
Nils