Once I see a pic, I could come up with a few names maybe. But, as far as the Arabian Horse Association is concerned, if you want the foal to be registered as a 1/2 Arabian, then you can only breed her back to a pure bred Arabian Stallion.
Her sire, Aploz +// was a several time US National Champ Country English Pleasure Horse. Is she a saddle seat mare? Trots big or no? That would also kind of narrow down a suitable stallion, even of the pure bred Arabs.
Can you post her dam line (AHA only gives the dam's name, not her pedigree)? So I can see who she is from on the Saddlebred side? Looking forward to pics, I LOVE NSH horses.