What have you done in researching census information? Do you have a good source of census data? Ancestry has only partial listings, but approximately 60 listings for BEAUCHAMP in Somerset 1841 are enough to warrant further investigations.
http://www.ancestry.com/search

Additional census details will help establish family groups and familial locations, if not in Kilmersdon itself, then somewhere nearby. Such locations may be significant. The census lists an Isaac BEAUCHAMP <1786> but I found no corresponding person in the LDS listings. This is no surprise as it is known that only a small portion of the LDS films have been transcribed into internet listings. Much of the data for Kilmersdon itself is apparently not transcribed. Susan’s marriage and that of Isaac and Anne Miles also in 1834, although they are IGIs, are also contributed information. And while they are quite probably accurate, they do not provide the documentary source that one finds with the extracted listings. Because the IGIs were previously open to contributed data, it is important to check the source information. It has only been recently, though perhaps before the start of your investigations, that the IGIs were closed and contributed data now goes to the pedigree files.

Your data beginning with John in 1826 is still a bit outside the time frame for Susan <1813> or perhaps Zebedee BEACHAM <1810>. What is the reason that you have nothing in Kilmersdon before 1826? Ideally in this so-called information age, one would take the most likely prospects from the census listings and cross match them with information from the corresponding parish registers. In reality it is more of a matter of finding what steps are necessary to gain access to these data sources. Have you tried the Somerset Record Office in Taunton?

Regards,
KA