I think the main reason why your begonias rotted on the capillary matting is simply, and notwithstanding your efforts, because that's not their natural environment.
We make a lot of mistakes, have a lot of disappointments (like trying to grow tomatoes outside in our climate) because we forget that basically plants in nature 'choose' where they want to grow.
In the biological-dynamical science of agriculture, weeds are an indication of what the earth needs, so that when the weeds die off the soil's missing elements, inherent in the dead weeds will be returned to the earth.
Whether water gets to the roots from above or below isn't the deciding factor - for instance palm trees have a special capillary system allowing water to be taken from below. So they wouldn't benefit from rainfall until the rain has soaked into the ground.
The last time I was in Tenerife I walked along a pavement where fruiting tomato plants were growing out of the cracks in the pavement!
So stick as near as you can to nature.
By the way, I've had a lot of success with various seedlings and seeds by putting them direct into earth specifically sold for geraniums: cucmbers, zuchetti, tomatoes, peas and lettuce.