I have collected several old (for the US) landscape yews and junipers over the past few years, and I haven't paid a cent to collect any of them. Once or twice I bought a bag of topsoil at Home Depot to fill in the holes, but that's it. In many cases, I think owners of older houses with old boring foundation plantings of yew and juniper, and sometimes old hedges, as well, do not really like them, and they are thrilled if someone will wrestle them out of the ground at no cost to themselves. So, only offer money as a last resort.
As for your question about digging up privets in the summer: Our summer weather in St. Louis probably isn't quite as brutal as yours in Texas, but it is pretty brutal. I dug out an entire old privet hedge in July last year; I didn't have time to pot all of them up immediately, so some just lived in their little clumps of collected dirt--in full sun--for weeks. One of them is still just sitting in its clump of collected dirt, nearly a year later, still in full sun, and it looks perfectly happy. I think it may be nearly impossible to kill these things. Give it a shot, especially if you can't wait until a more appropriate collecting time for your area.