I glanced over your first thread and decided to try softening veggies in the fridge which worked a lot easier (quicker) than I expected. I tried this with carrots, celery and cabbage.
I did it by putting veggies in fridge at 34*F in a drawer without any cover. It took a week for them to soften.
Overall not bad, i didn't detect any flavor loss by what I tasted. They were generally soft, you could bend the veggies but they could snap..eventually. Carrots (only the thin ones) were hard to peel and would wrinkle, but looked alright once peeled.
As for cutting the veggies it was smoooooth, I could cut the carrots really thin but I chose to cut them lengthwise, with a thickness that was slightly translucent. There was some really interesting chew to them..thick with a slight crunch. Even cutting cubbed for my stocks/broths it felt nice. Celery was fine, not really a noticeable difference in any regard. The cabbage though was really the best. I think because when I used it for Asian noodle dishes cutting the cabbage thin required no cook time and they tasted fresh and great, maybe because the hot soup freshened them up..? Also I made a side dish of some cabbage with sausage and the cook time was also reduced by almost half...so A+ for saving some gas.
Practically, saving veggies for a week doesn't sound ideal, but cutting those carrots was like driving a nice car on a nice road.