Those are some lovely pieces indeed, thank you very much for posting those pics !
As to the provenance of the original saber(s) I'd say it could be both Hungarian or Venetian (or even Balkan in origin) - Venice had a considerable influence on Hungaro-Balkan arms and amour (the blade however would be after the Turkish fashion of course).. I imagine that such a saber could easily have been carried by either a period Hungarian Hussar, Venetian Stradiot or even a Rumelian (european) Ottoman trooper.. Do note also the slightly canted handle on some pieces as well.. Many of the men serving in those units were often of mixed heritage that is Serb/Magyar (early hussars) , Albanian/Greek (stradiots) to name a few.. During the period in questions these nations were heavily influenced by both North Italian as well as Ottoman Turkish trends. A result of this mating can be imho quite clearly seen in those transitional sabers.
I recently spotted a somewhat similar depiction of a saber in an Altair painting back home in our church (Bardejov, Slovakia , former Upper Hungary) dated to 1480s - depicting a scene with a byzantine emperor Heraclius...
data from imareal:
Kunstwerk: Temperamalerei-Holz ; Einrichtung sakral ; Flügelaltar Kreuzigungsaltar ; Slowakei ; Kreuzerhöhung:03:016-027
Dokumentation: 1480 ; 1490 ; Bardejov ; Slowakei ; Pfarrkirche St. Ägidius
Anmerkungen: 700x800 ; Bardejov ; Libuse Cidlinska, Goticke kridlove oltare na Slovensku, 1989, S. 30f
Closeups done by myself:
(note the S or almost figure 8 shaped cross-guard, I believe some authors calls this "schiavonesca" style, afaik such curved quilllons were not only restricted to those weapons only)
Collection of XV. century sabres from Budapest National Museum (source: Régi Magyar Fegyverek by Kalmár János):
Some more from B.N.M - courtesy of http://museum.velizariy.kiev.ua
(closeup on yelmen)