Unfortunately, the digitized records available from Matricula seem to be of little help due to the restrictions placed on which records could be filmed and which ones could be viewed. Kein Ruhmesblatt für Österreich! it is a mess. However, the scans themselves are of high quality.
I did browse the Matricula records for Kremsmünster, mostly the indexes for 1750 - 1900. It was surprising how few the records were for your key name Jungreithmayr and its variations. The birth index mentions Johann, born 1883, Katharina, born 1883 who died in 1890 or 93, Franz, born 1885, Rosina, born 1886 who died 1887, and Anna Maria, born 1889 who died in the same year.
The death index shows Anna Maria and Rosina, interestingly with addresses, i.e., Kremsegg 26 for Rosina and Kremsegg 12 for Anna. This may indicate that the births happened in two families, or that the family moved houses.
The marriage index mentions the wedding in 1860 of Klara (or is it Maria?) Jungreithmayr to Johann Aichinger. Unfortunately, the record itself has not been digitized (same thing with the birth index entries mentioned above).
However, there was one marriage for which the record is also available. This was in the year 1783. The groom was Georg Jungreithmayr, a widower. The bride was Elisabeth Edlbaum or Edelbaum. Best men were Johann Jungreithmayr and Philipp Jungreithmayr. It appears to me that the towns where the witnesses came from are mentioned but reading them is difficult. The marriage entry seems to say - although the record is in the Roman-catholic records - that the wedding took place in the (Lutheran) prayer house in Schaden and was officiated by a Lutheran preacher who came from Eferding. (The Tolerance Edict allowing Lutherans and other religions had been issued in 1881 by Emperor Joseph II.) Therefore, it seems that at least some branches of your Jungreithmayrs in the Kremsmünster area were Lutherans. This would explain the gaps in the indexes.
What are the details you have about your ancestors? It might be best for you to order the LDS microfilms of the duplicates of the Roman-catholic records of Kremsmünster which cover the time back to 1811. Also, try to find out where the Lutheran records for Kremsmünster and Scharten are kept.
The indexes mentioned another family name, Jungmayr, which may well have some meaning (in its possible relation to your name).
Kremsegg is a village near Kremsmünster.
As for spelling variations, the Kremsmünster matrikels have Jungreithmayr and Jungreithmair. I may have overlooked others.