Naturalization for parent who was child while a Hungarian citizen

Hi there!  First, let me say that this is an extremely helpful blog.  I'm learning so much just reading about everyone's experiences.  Of course, nothing in citizenship issues is cut and dry and, therefore, I have a complicated question. 

My late father was born in the United States, but he was sent to live with his grandparents in Austria when he was one year old.  He lived there for 9 years.  Then WWI came to the region and he was returned to the U.S. for his safety.  That region of Austria, I learned, fell under the "Republic of Hungary" during that timeline so, technically, he would have qualified for Hungarian citizenship.  However, he was never "naturalized" to my knowledge.  He would have mentioned this, I'm sure, if he had even known such a process took place.  He did not serve in the military in the U.S. and the Hungarian consulate confirmed he would have qualified as a citizen. However, I need paperwork to back this up, such as the simple naturalization.  I assume there is other acceptable paperwork.

The Austrian consulate said that the records from that region (census, etc.) that might show his time there were nearly entirely obliterated by fires during the war, so it is doubtful I can find anything about him being naturalized officially, even if he was.  The Hungarian consulate (who has been wonderfully kind and helpful) said he would have been a Hungarian citizen, but I'd need to find out about the naturalization.

I'm not as concerned about the language issue because that is something that I can learn (suggestions welcome, btw) and I grew up around all his Hungarian friends, so I have reasonable knowledge of the culture.  Is there any way that anyone here can think of that would help provide official paperwork regarding his citizenship that the consulate would be able to accept?   

I have wanted, all my life, to be in Europe and I remember his stories of the region so vividly, as well as that of his friends.  I never imagined there would be an opportunity for me to gain citizenship in Europe and it would be painful for it to slip away over some small technicality with paperwork (although I'm far from the only person who has experienced that in life).   I've visited the area several times and was repeatedly told (by the Austrians) that there are no records.  The only record I have of that time period is the ship's passenger log of his return ot the United States.  And, sadly, anyone who can verify any of the information of his time there has long passed away. 

Do I have any hope?