Report from Paul Schmidt on Esch research in German records at Salt Lake. Wording is quoted from his report except where in [brackets]. Those comments are mine based on things he wrote that didn't need to be quoted exactly.
[Correction of previous Adam-Catherine marriage translation - I had "of here" and that is not accurate. "The phrase used was daselbst which is actually translateds as "from there", or "of that place", meaning Blessenbach.]
[Misc notes, out of order] - Henrich is a regional form of Heinrich. The suffix, "EN" is added to the name to show possession, such as "Johan Henrich Esch's son". The suffix, "IN" denotes a feminine ending of the surname, and generally can be ignored. Although I was unable to positively tie this family to your Adam Ash, I'm virtually certain that this relationship is correct. It's too bad that one of the most crucial parish registers is missing, but that's what happens sometimes.
[The important, analysis part of his report] - Therefore, research began in Blessenbach, where most of the family of Johann Heinrich Esch was identified and documented. Unfortunately, there appears to be a rigester missing, for the years 1742-64, so the christening of the ancestral Johann Adam Esch (and possibly younger siblings) could not be procured. To further complicate matters, some of the children born to Johann Henrich Esch were not named in the records. Generally, children were named after one or more of their godparents (or sponsors), so the unnamed child born in 1727 may have been named Christoph, and the child born in 1732 could have been Johann Adam or Johann Wilhelm, although the gender of the child was not provided in either entry. [It couldn't have been Adam because Adam was born in 1744]. If William Ash was a brother of Adam, he would have to have been the child born in 1732. If born after 1741, it is unlikely that he would have been able to emigrate on his own in 1753/54.
Since this was the only Johann Henrich Esch residing in Blessenbach, he almost certainly was the ancestor. It is highly unlikely that another man by that name moved to the parish after 741 and began having children.
[I am now convinced that Adam was indeed a much younger brother to Henry and William because Adam's marriage record shows his father is Johann Henrich, Henry's birth record shows his father has the same name, and there is only one man of that name in the parish, and that man had children spanning the years up close to Adam's birth.]
[The rest of the report just shows the methodology to find the records that are now placed in the family groups.]
[Lastly, he says:] The family may have originated in nearby Eppenrod, and those registers can be searched further for them during a future session, if desired. [The Kroh, Zimmer, and Jost surnames could also be searched; and we should find out from Blessenbach itself if the missing register has been found since the others were microfilmed.]