Back when I used to pick all of our greenish/blush tomatoes just before our first killing frost (it's been years, today the plants die long before a frost) I'd place them on a table on newspaper in a spare room to ripen up on their own. There would be a few that would show signs of decay but those got tossed out asap, but most ripened up ok-ish. Most of the tomatoes that were picked totally green would eventually turn red but those would be of poor store-bought quality (not vine ripened).

Another trick is to place the unripe tomatoes into a large paper bag with an apple inside to speed up the color change. This doesn't help with quality, but it works. The apples let off ethylene gas which can help turn the tomatoes red, it's the method used by tomato dealers, they should be ashamed of themselves, ha.

ps, sorry about your tree damage, we've been lucky here with only 4 power outages over the past few weeks, no damage, but folks all over the country, and world for that matter, have taken it very hard on the chin this year.

I haven't noticed many rotting when picked at blush. What sent my antenna up is your leaves turning brown while many tomatoes remain. I suggest asking around your area to see if some vines stay green longer than yours. If so you likly have disease and need to rotate ground. Don't bet the farm on what I say because I'm in deep South where it might wrk different. My vines continue to bloom but don't set fruit when tempature hits 90f. After that vines remain green as fruit ripens then turn brown at 100f after 95% fruit has been hearvested. I've seen what you discribe and it's usually because of disease.