Army Ordnance officers recommended a solid frame revolver as the hinged frame S&W revolvers weren't working out so well in the durability department during testing and trial issues of 1872, but neither did the open top Colts work as well as hoped for either hence the reason for the Ordnance request.
I believe the Rollin White patent expired in 1868 and Colt did release the Open Top 1860 conversion revolvers shortly after.
These competed with the S&W American revolver in those trials of 1871-72
Colt had the Thuer front loading cartridge revolver prior to that but it was no smashing success by any means.
No one person designed the Model P "Strap pistol" as a whole.
A team of engineers came up with the concept, designed the tooling, made the prototypes, and got the thing into production.HTH