First

Manage/SledgeHammer to my knowledge was never listed for use around edibles.

Second

everytime I have used that stuff, as labelled, I must give up on that area for at least a year. Otherwise plants that follow grow poorly if at all.

Other products labeled for nutsedge contain arsenic within their moluclar structure. I am not sure if Manage does or doesnt but again it is NOT labelled for use around edibles.

In the short term pulling does create some off shoots but in the long term, and IF you are vigilant about pulling, you will eventually exhaust the plant of resources and it will fade into obscurity (this could be a few years). What you DO NOT want to let it do is go to seed. That's is how you will ruin your efforts on pulling.

if you have a raised bed there is a task you can do IF you want to spend the time doing it. Get a series of hardware cloth screens and screen the soil by hand to remove the roots and "nuts". This is exhaustive work but you will seriously reduce the population assuming there are no seeds in the soil.

Generally I have just taken to removing the soil completely to a depth of about 18" and then replacing it with new soil .

No easy way to get rid of the stuff around edibles. I have seen it poke through IRT Mulch even so hard work and diligence is the only way I know.