In the files I have Abraham's father is stated as Michael Kurtz and mother Elizabeth Cober. This doesn't work with the land records I have found. There are only four Kurtz Ontario Land Records. Nicholas, Abraham, and John C. and James Kurtz (joint application). Nicholas states he came to Upper Canada recently (year of application is 1805). States he has a wife and 8 children most of whom are grown. In 1818 Abraham applies to purchase land and states he has been in the area for 13 years which puts him back to the same time Nicholas states he came. There is the possiblity that Nicholas was a brother of Michael and Abraham came with them but it appears he may have been only about 14 years old. It is more likely that he is Nicholas' son. I have located a marriage between Nicholas Kurtz and Elizabeth Shelly about 1875 Bucks Co. Penn.
If there is "evidence" as to Abraham's father then it will solve the mystery.
One thing that isn't in question is that the Kurtz family we know here isn't listed anywhere in the numerous records I have as a Loyalist. Any Loyalist states it with a claim for damages to get free land. If they fought in the militia it is strongly stated. That got you free land as well. I am putting Nicholas and Abraham's applications below.