I like the concept of formal rigid merging with the informal .....

B-thumb,
I think you can pull off the marriage of the two distinctly looking styles by the way you design the integration.

If you just stop one and then start the other without a 'linking sequence' or a uniting design, it will look disjointed.

By extending one pattern into the other you will have better success in the union.

I'll try to dig up a photo in my archives, it may take me a couple days, but I know I've got a sample that may help you design your own unique design.
Sometimes seeing how others have handled this problem is an inspirational springboard for you to come up with your own solution.

It can be done ... look at some modernist paintings, as Mich says find a way to make an interesting intersection.
If yo do use a distinct line between the two, this will set the two spaces off as different spaces. So in the case of a landing it can act like a door mat acts or a stoop (it can help make you comfortably pause at the bottom of the staires if you want that to happen ... as a special place distinct from the walkway. In this case you might use some sort of divider.... Like small pieces of bluestone turned on edge or other sorts of shapes or a different stone altogether.
Re stone dust etc. these are regional terms, basically you can use .25inch minus gravel --- decomposed granite is pretty much the same as chicken grit, to which, I bet, an Oklahoma boy has access.
"Will the saws pull it off?" what did you mean by this, aesthetics or mechanic-
A

i saw this done, where irregular fieldstone and small cobbles were mixed into a patio of cut stones and pavers,
also there were holes for plants to grow in. personally I liked the look of it. The owners had extended to patio into a small walkway as well. But I wondered how the odd
stones effected people walking. But from what i could see the ankle benders were kept out of the way of main traffic flow.