Ariel, any question put forward by you would never be considered stupid! quite the contrary! I know very well how disappointing it is when a post goes unanswered, so without doing my usual marathon of research I will just place tentative comments pending further detail.
The style of quillons drooping downward have of course brought forth the pragmatic idea that these were intended to catch and stop the opponents blade in sword to sword combat, and that hilts with more developed quillon systems followed.
In the middle ages, the term 'quillon' did not exist, and the broadsword was mounted with simple horizontal bar known as the crossguard. During the crusades this was known as the 'cross', and of course the imagery of these times noted the sword as in the image of the Holy Cross.
It would be tempting to suggest that the Islamic swords had thier guards fashioned dropping downward to move away from that representation, however unlikely the idea, it seemed worthy of note. Having brought in that suggestion, it should be noted that the drooping quillon was also quite well known in Europe and the multiple downward quillons arrangement is seen on the 'crab claw' hilts as well as simple downward quillons seen on French and Italian medieval broadswords as well.
The Hispano-Moresque jineta was likely a product of influences with Italy and France, and it seems more probable that that influence was most probably induced to the jineta much in the way that the stortas and hilts of Italy influenced development of the 'nimcha' hilt in the Maghreb.
The downward projection on the earlier form of kattara in Oman would seem to have also reflected the effect of the hilts seen on the early swords of Islam of which I believe many were remounted with these form hilts.
The Zanzibari nimchas seem to have also borne the influence of Italian swords, particularly with the ring on the crossguard.
While many scholars will take the pragmatic approach, and suggest this characteristic of these hilts as a combat improvement, some will take the romanticized concept related to the cross into serious consideration. From an artists or historians view, perhaps the style of turning down the quillon was simply a variant design to be aesthetically pleasing.
Whatever the case may be for the reason of the downward quillon, its diffusion seems most likely like that of most weapons, following trade and warfare.
I hope this perspective offering my own opinions may bring forth others, and as always I welcome other views.
It was a good question, so lets hear em !
All best regards,
Jim