There are several possible entirely valid places to go after the 1K diamond plates, really. You can go on to the Chosera waterstones, the ceramics, stropping on various materials with various abrasives, or any one of another half dozen options from second-source vendors like Ken over at CKTG. Examples there would be Shapton waterstones, diamond films in a wide array of grits, nubatama waterstones, and a number of other stropping materials.
And yeah, the strops DO continue the work, both in terms of removing burr, and polishing the edge. Bear in mind that a certain size of abrasive on a strop will result in an entirely different finish than that same abrasive on a solid backing (like a stone).