Laura:
I have tested with Ancestry DNA and Family Tree DNA. You can also test with 23 and Me and My Hertiage and I'm sure there are a few other companies.
Ancestry by far has the biggest data base but I find that Ancestry matches frequently do not get back to you when you try to make contact.
Regardless of who you test with, make sure you add your data to the Gedmatch data base www.gedmatch.com to expand your matching pool.
I did some more searching on the subscription site Roots Ireland and it appears that John Davoren/Davern and Honor Linnane had at least ten children as follows:
Bridget April 1863 Ellen December 1864 Mary January 1867 Catherine March 1869 Bartholomew 1873 Honor October 1875 Martin January 1878 John January 1880 Anne August 1882 Susan November 1884
I searched for marriages and deaths in the Gort registration district and only found one possible family record which was a death record for an Ellen in 1894. Now your Ellen should have been 29 yet this record shows 22. The informant was a brother Martin which matches one of the siblings so I'm not sure.
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
You mentioned finding Bartley in the 1911 census. Is he the married Bartley in the Oranmore area?
I did not see any of your family around Mulroog in the 1901 or 1911 censuses.
Roger