As to the origin, many do not seem to remember that Peabody was NOT the iventor of the rear-pivoting breechblock - there was another one before.
And to give credit where due, the martini mod really is what made the difference - maybe not in the US, but it probably was the most successful action design of the day, still being made today.
Royalties?  Kinda asking J.M. Browning to pay royalties to Sharps because he also used a dropping block on his 1885.
And as to the Turk rifles, Providence tool actually paid royalties to Martini for using his patent...  They rebutted Henry's demand because his patent already had expired.
Mind you, I have one of the Porvidence tool Turkish rifles, and it is a pretty nice one - very accurate too.  Nice cartridge indeed...

Inventor, that's a good question - but there was a combustible cartridge breechloader carbine design with rear-pivoting breechblock before Peabody's design.  I don't have my reference book handy (Malcolm Cobb, the Martini Henry notebook), or I could give you a name.  Does that make him the inventor?  Hardly, who knows what was made even earlier...