Is it possible that a sibling of Rudolf, or a sibling of Anna, ended up in Gmunden either due to his/her career or by marriage? So far, I see no reason that would point to Gmunden based on the Kollerschlag matrikels. Gmunden is a famous tourist town in the so-called Salzkammergut. It is far away from Kollerschlag/Haselbach, literally on the opposite end of Upper Austria.
Let me add to the comments I had made about the vital records called matrikels in Austria. The oldest of them go back to about 1600. In the 1780s, emperor Joseph II vested the churches with the responsibility to create and maintain the vital records of the population on behalf of the state. In the early to mid 1800s, parishes were required not only to keep the vital records, but also produce a duplicate that was after year-end sent to the diocesan office. The microfilms at the State Archive of Upper Austria in Linz (and the ones available from LDS) are of the duplicates. Compared to the originals, the duplicates have a few disadvantages such as (a) they only go back to the year 1819 when they started to be required by the diocese Linz, (b) they have occasional copying errors as they were sometimes produced in haste after the year was over, and (c) they lack the marginal notes which were often added to an original birth entry after many years, such as when, whom, and where the person married, or died. Still, it is vastly better to have microfilms or digitized versions of the duplicates than having to travel to the parishes or the Diocesan Archive in order to take a look at the original matrikels.
As for the records of Roman-catholics in Upper Austria, microfilms of the duplicates can be ordered and viewed at an LDS Family History Library near where you live. As stated above, they go back to 1819. In the Matricula effort of digitizing the Roman-catholic records of Upper Austria and making them available for on-line viewing, it is possible, I believe, that the long-existing issue came up of who is the real owner of those records that are dated before 1785 versus the ones after 1785, and the level of access to the records which should be provided to family searchers. For recent vital records, data privacy laws compound the difficulties regarding access to the records. So, how do the digital images of the Matricula effort fit in? I thank Mr. Josef Weichenberger of the State Archive of Upper Austria for the following explanations. Matricula was allowed to film all original matrikel books which were dated 1820 or earlier. If any record in the book was dated 1820 or higher, the book was not digitized. Fortunately, though, all index books were digitized regardless of age. However, general access to them is not available if they reach into the most recent times where the data privacy concerns kick in. These concerns affect birth records more than marriage records and death records. The most recent records one can access are death records. Since the 1820 rule prevented many matrikels from Upper Austria from being digitized, the State Archive started an additional project to digitize the duplicates (the ones already on microfilm). This effort is supposed to be finished by the end of this year. By the way, searching for ancestors of the same bloodline is a valid reason to ask for an exception from the privacy laws.
When I tried to give you a hand last week in browsing the Matricula records of Kollerschlag and Sarleinsbach, it was frustrating as there was a technical glitch which made the loading of pages extremely time-consuming. The other problem was that the most interesting matrikels for your initial search are from about 1900 which have not been digitized, and where in most cases even the indices are not accessible. Nevertheless, on cursory first browsing, the information found looks very interesting, as summarized now.
Kollerschlag, index to the death records from 1892 and later:
Rudolf Christl, died on Feb. 27 or 28, 1940, resident at house Haselbach No. 8
Franziska Christl, on August 7, 1946, same address
Erich Christl, on June 8, 1954, same address
Josef Christl, on July 19, 1986, same address
Berta Christl, on Sept. 21, 1989, resident at Haid
I think an initial working hypothesis would be to identify Rudolf and Franziska as your greatgrandparents. Could Erich be a brother of Rudolf, and Josef a son?
Kollerschlag, index to the death records before 1892:
Death of Georg Gristl, originally from Wegscheid, 1891
Kollerschlag, several birth index books:
Anna Maria Christl, born on August 28, 1830, parents resident at house Nebelberg 7
Anna Maria Christl, November 12, 1815, Kollerschlag No. 60
Johann Michael Christl, Oct. 19, 1818, Kollerschlag 2
Franziska Christl, Dec. 12, 1820, Kollerschlag 39
Paul Christl, July 4, 1825, Kollerschlag 35
Johann Christl, May 23, 1833, Kollerschlag 18
Anton Christl, June 11, 1846, Kollerschlag 3
Michael Christl, Sept. 29, 1859, Kollerschlag 6
Rudolf Christl, 1861, Kollerschlag
L(... illegible, Lorenzmartin?) Christl, 1863, Kollerschlag
Anton Christl, 1866, Kollerschlag
Maria Christl, 1869, Kollerschlag
Katharina Christl, 1872, Haselbach
Ludwig Christl, 1875, Haselbach
Maybe these are (parts of) two generations of your bloodline. The Rudolf born in 1861 is likely your greatgrandfather. The age fits the Ellis Island record. Michael and the last 5 births could all be siblings of Rudolf. From the many addresses one can also preliminarily guess that the family had no steady home until they moved to Haselbach house no. 8 around the year 1870. Your ancestors were not wealthy but they survived. Haselbach 8 was a house with no or little land (i.e., no farm). The family that lived there before your Christls, had the name Lang and were foresters.
I am once again running out of time. The rest of my comments follows soon, hopefully tomorrow.