I don't know who told you trapping and relocating a bear is humane, but it isn't. First off, you're trapping that animal, and dumping it someplace else. Very likely into some other bears territory that isn't going to take kindly to sharing with an intruder, especially if it's another male bear. If it had worms, was ill, or had some other transmissible disease, guess what? Now you've possibly introduced a problem to the other animals in the area it was released to. A bear will quite often rapidly return to it's home. Sometimes covering hundreds of miles in a matter of days, especially if the food there was especially great.
I lived in the redding area for a number of years, and I know of problem bears who were trapped. You know what happened to them? They either returned in two days from where they'd been dumped, or they decided that raiding the human food sources near where they were dumped was great idea, and got killed when an irate farmer discovered them destroying livestock or other property. I know where they were dumping the bears, and the people living in the area who had to deal with the problem bears weren't thrilled at inheriting someone elses problem. Fish and Game (Scuse me. Fish and Wildlife. *eyeroll*) is lazy, and seems to rely on this exact situation. They do it mostly to appease the public operating under the illusion the bear gets to live happy and free. Sorry for soap-boxing the issue, but it's an area I'm very familiar with, and an issue near and dear to my heart.
The only way to deal with problem bears is to hurt them so bad they don't want to chance it again, or to kill them. The absolute best way to avoid problem bears is not allowing situations where they can discover ways to become a problem.It is perfectly legal to hunt black bear in California. Frankly for me, it was far more reliable to find bear than deer (I think it tastes better, too.) YOu made it clear you don't want to hurt the bears, I get it. A bear tag is merely a legal means to an end, if and only if push came to shove, sparing you any fish and game trouble. And possibly yummies to line your freezer with, since you don't waste game.
That said. I am very sorry about your job situation. Is there a possibility of moving your chickens to a relatives place or a friend until you can deal with the fencing situation? It isn't ideal I know, but would be a lot safer since the bears have already torn up one coop nearby. Might I ask what your husband does for a living? I still have some friends and family in the area. I can ask them about jobs they know of.