I've always picked at blush and before they ripen they always have spots and funk develop and get tossed out. Often it looks like anthracnose even though the tomatoes are free of it (at least to the naked eye) when they're brought in. So I'm thinking the only option is to let them get a little farther along in ripening so there's less time between coming in, gathering enough tomatoes to do the canning and then doing the actual canning. The plants also get a regular fungicide spray, mostly Serenade and occasionally Daconil.
I'm tired of seeing all the hard work go to the compost pile so this year I'm trying this. The birds have a bird bath nearby. Last year I put one right at the tomato row. Couldn't be any closer yet they preferred the tomatoes!