Exactly Joe, lots of speculation and generally accepted ideas, but without hard evidence these remain inconclusive, though quite plausible.
Sir Richard Burton, a pioneer in edged weapons research wrote in 1884 ("Book of the Sword", p.139 ), "...the old Persian sword, often called by mistake the Turkish sword, ends in a point beyond a broadening of the blade. The effect is to add force to the cut; the weapon becomes top heavy, but that is of little consequence when only a single slash, and no guarding is required of it. This peculiarity was curiously developed in the true Turkish scymitar, which we see in every picture of the sixteenth century...".
Naturally, we know that Burton's work has been tremendously superceded, and that he is describing the yelman, and that this feature was quite well known in Europe on various forms of falchion long before and during the 16th century and certainly concurrent in that period with Turkish forms.
While these falchions do not necessarily correspond to the blade profile with yelman, they do carry blades dramatically widened toward the tip, and usually radiused rather than the step type widening from the back edge.
In "European and American Arms" by Claude Blair (1962), the following falchions are shown....a German falchion of early 15th c. (#40) ; the parade sabre of Archduke Ferdinand of Tyrol c.1560 Italian ; Brescian falchion (#161) of mid 16th c. ; the Conyers falchion from Durham Cathedral c.1260-70 (#21).
The development of the sabre prior to these times seems the most disputed, though as noted, has been discussed and written on considerably.
Great photos!
What are the sources?
The first one has a blade that seems more 19th century, is it identified in the source as Polish? It seems a bit heavy for a Polish sabre.
The last English 'scimitar' I would agree is latter 19th c. and corresponds with decorative items produced in that period. While the huge blade somewhat reflects some of the early falchions, it seems to also parallel the huge 'dadao' blades of so called 'oxtail ' form that were widely seen in China during the "Boxer Rebellion" of 1900, though these swords had been in use long prior to this. The crossguard seems very much like those on kaskaras, and the grip and pommel recall certain medieval style. Is this from a collection?
All best regards,
Jim