If you go on the Lazarus website click on Nyitra megye/ Nitra county that Hosszufalu there is now called Dlha nad Vahom. If you click on Pozsony megye that village Dlha has a name Felsohosszufalu. Both villages had the name Hosszufalu, Hoszufalu.
The LDS website is showing films for Dlha nad Vahom, Roman Catholic church.
Can you e-mail a scanned copy of the certificate to my e-mail?I would like to take a look at the godparents names as the way you have them they do not make sense.