The most important part in cleaning this is
Check the backing , is it Jute?
if so use the least amount of water or encap (preferred).
if synthetic then your idea is not bad. just dont be too aggressive with bonnet
I have cleaned these types of wool runners without any issues
use a wool certified or at least Ph balance prespray but NO ENZYMES!, gently agitate and rinse With low temperature, do plenty of dry strokes and have a clean terry cloth towel to wipe up any water. Give the customer drying instructions. I like to clean wool with low temperature and low PSI usually 200 psi, rinses best and leaves least amount of moisture.