The OP's hope of not using chemicals, and substituting mechanical results in EXACTLY the opposite results desired.
EVERY time you disturb whatever is under the gravel, you are actually creating a seed bed to sprout the seeds.
I use a type of stone that is similar to what many call "crusher run",
except, what I use has a different type of "fines" in it.
This stuff packs so close to concrete, the results are amazing.
Virginia DOT uses the stuff as a sub-base for new asphalt roads.
All I know, is that it stays put, even on grades, and turns,, and weeds struggle mightily to survive,,,
Once it is in place, I work REALLY hard to resist grading it,,
the less it is worked, the less weeds grow.
If I get some grass,, etc, usually driving over it a couple times will eliminate it.
So, grass in the middle usually requires running over it with a narrow tractor, like my JD 650,,
This DIY roller kills grass (weak grass) in dry conditions.
I pull it at about the max speed of the 650.
The roller is also great for compacting the stuff, and it compacts,, A LOT!