If you see no/hardly any run off, it is maybe better to plow your swales.
I have never tried it myself before but if I would get a sloping piece of land in my area, that is what I would do (they tend to make white glass from my sub-soil

)
The burning could work, but bringing in ashes from your cooking fire might also do the trick and requires probably less kgs of material transported. Maybe even make a very rough
compost with wood chips (or other material) and ashes?
My plan of attack (I have one parcel that has 2m slope on 50m) is to plant asparagus in the middle
[edit]and for some reason, unknown to me, the post didn't went online so now it's maybe a little lame but anyway, it's a different method again