Results of the wood ash were definitely negative for me. Not one of the tomatoes in those containers had sweet fruit, although they are all from sweet tomato lines - siblings in untreated pots were as sweet as ever and beat the taste tests hands down.
I used the wood ash instead of lime, in my case I use lime every year and it seems to be a good thing even in containers, the condition of being watered so often is just like outdoors, there is a tendency for the soil to acidify over time in this climate and needs to be pushed back (we have no calcium in our soil here either).
Now it is a fact that potassium directly affects tomato sweetness, and potassium deficiencies are also the cause of fruit defects as Coastal described - white flesh, uneven ripening. There are a lot of factors that can affect potassium uptake (too much sun, not enough sun, soil temperature too hot or too cold, pH too low or too high.) We know that wood ash is rich in potassium, but is it not accessible to the plants because of the high pH? Seems to me that the amount you'd have to add to gain potassium as a nutrient could also put your pH out of whack - at least, that would explain what happened. Or maybe it's a thing with the peat in container mixes. Maybe potassium gets locked up with the high pH, needs a change of conditions to make it available...
