COme on, you have an infinite amount of a much stronger alkali under your pots and pans there. Just dissolve the white ash in water, decant, filter, evaporate the clear liquid, and voilà! Pure pot ash, which is perfect for soap making, especially with that olive oil you just found the other day.
When I had a hearth, I used to dissolve, decant and filter my ashes and keep the liquid as a laundry detergent. Costed nothing, and you neutralize the alkali by putting cheap distilled vinegar in the softener compartment. Maybe don't wash your delicates with that as it's surprisingly strong, but the laundry smelled goooood
God I wish I could afford a house.