At my house, hardwood cuttings work even better than soft wood... I can take large diameter sticks and bury lengths which become new bushes...
Spreading ripe seeds at my house often simply provides food for the rodents and the birds... Tends to be hit or miss for me, but I get genetic drift, and different coloured flowers from seed, so... it's worth it to keep trying.
While vitex usually will survive drought conditions, it's not a good time to propagate them, or move them. Far better to wait until winter.
I'm not sure that fertilizing them is necessary, and it's always a bad idea to fertilize in the drought,
All I ever do for my vitex is spread woodchips around them...