I would go with Halosulfuron. It is shorter-lived than trifloxysulfuron and has some veggies on the label. Sulfosulfuron is very short-lived also, but not sure if there is a label for garden plants. How long really depends on what you plant. You likely will need to treat the nutsedge a second time, but a month may work, again depending on what you plant.

If you do the things you need to do when you need to do them then someday you can do the things you want to do when you want to do them.