Well, these are are pictures of either Monghols or the Persians fighting the Monghol-related warriors, and the Yelman-bearing swords do not belong to Persians, do they?
In his monumental treatise"Arms and Armor from Iran", Mr. Khorasani presented all kinds of swords he considered Persian (throwing in some Uzbeki and Indian stuff for good measure), but even he did not claim the Persian origin for any of the early Yelman swords. There is such thing as Indian Gaddara ( with Yelman), but all I have seen are ~18- 19th century.
The swords you showed earlier are mostly Mameluke ( which was my point).
We have no idea whether there were any Ottoman Yelman-bearing Kilijes ( Yusel must have known what he was talking about
), but as you have noticed there were examples of similar Mameluke swords even in the 13th century.
Likely, the Yelman-ed swords originated in China or Central Asia, but they surely did not have any influence on Persian weapons and unlikely to pass down the "Persian route".
In the absense of the Ottoman evidence, one wonders whether Yelman-ed swords found their way to the Mamelukes from Central Asia along the westward route, ie with the Kipchaks who formed the bulk of the Mameluke army.