just out of curiosity...... What would you do with the tamarind harvest if you could indeed grow tamarind tree in California?

One thing that Tamarinds need is a dry season (dry winter). Cold and wet would be the end of them.

I have about 40 tamarind trees, the largest is about 10 metres tall. What to do with the harvest? I leave it to the birds. They're a nice looking tree to have around the place, and good to have some fruit available.

Like any edibles, eat them. The tree itself is attractive. I did find that there is one growing and fruiting in Fullerton's magic climate. In good years-hot summers- they ripen,in most years they are not as sweet.
I grew one from seed..and it poked along until I placed it in a greenhouse,where of course it thrived.

In the caribbean its can be used to make drink/juice its packed with Vitamin c also roll the fruit in sugar or boil it remove the acid water make drink with that then add lots and lots or sugar to the cooked mix and its delicious