[Jim McDougall]

These are pretty amazing sabers JT, and frankly seldom acquired by other than the most discerning collectors. While in my earlier days I did have one with the usual ivory mameluke style hilt, I regarded it as the 1831 pattern for staff officers (Robson, 1975). It was apparently through one of the outfitters in India, which seem most often in Calcutta (it may have been Harman, but of course Manton was more prevalent).

Actually Richard Dellar does address a number of these type officers 'mameluke' hilts in "The British Cavalry Sword 1788-1912" the companion volume (2019) to his remarkable reference book earlier.
His references refer of course to specific examples and details pertaining to their owners, and outstanding photos of each example.
Many have the 'stepped' tip of the distal third of the blade, which was of course from the Turkic style blades of India and often on tulwar blades.

This blade feature became popular in England during the early development of the British regulation patterns, and especially with officers, whose carte blanche latitude with privately commissioned swords permitted such variations.

As you note, the mameluke style saber was much favored by both French and British officers after the Egyptian campaigns 1798-1802, and the trend to adopt the form became popular in following years. The early example you note was by Samuel Brunn, Charing Cross, London in 1805.
The 1822 regulations prescribed these style hilts for the newly formed lancer regiments (9th, 12th and 16th light cavalry).

These 'stepped' tip blades were being produced in Solingen for England in earlier years as seen in a number of officers sabers produced in the earlier years of the century. These seem to have been intended for EIC officers, but these blades were also used for the group of sabers (27) for the 10th Hussars in 1808.

It seems most likely your example has an Indian tulwar blade from India which reflects the style being reproduced in Germany for England as seen in these examples pictured, on the left is the 10th Hussar pattern. The group of these blades were in England some time before 1808 so it seems apparent Solingen was producing early in the century. The next is what is believed a somewhat limited type of saber believed for EIC about 1800 (as noted by Wilkinson).
At this point I would suggest this is a Turkic type blade from India rather than Ottoman, and a remarkable example using a tulwar blade. As far as I know these instances were quite unusual.