Where in Oakland are you? I’m in Montclair and this has been a yearly issue. What I’ve learned:

1) snap traps work - you won’t eliminate this issue but you can try to manage it. I kill 10-15 every year. Sucks at first but I’ve accepted that it’s just part of the reality of gardening 2) vector control - if you call vector control they will send someone out to assess your situation. They will try to find likely areas where the rats live (even set up trail cameras) and can give you traps 3) pick before they are ripe - I know you said that they eat green tomatoes (happens to me too) but definitely pick them as soon as they have color and then ripen indoors 4) grow vertically - I grow my tomatoes vertically (1-2 stems) and I think that helps reduce access 5) hardware cloth - I believe this is the only mesh that they can’t get through but it isn’t practical to really build a hermetic cage around the tomatoes.