Don’t snip the picked up sts as they form the first row of the sweater body. Rather you want to snip the edge of the hood or even a row up into the hood… That will leave intact sts on the body. You will have to pick out small pieces of yarn left from the hood but that’s relatively easy.
Save the live sts from the hood. You can always knit an extra row or two on the hood and bind off. Yes, you’ll have to sew a seam between the hood edge and the body.
To be absolutely sure why don’t you knit a swatch (about 15-20sts) with scrap yarn, bind off and then pick up sts as you did for the body. After a few rows, you can snip the hood part of the swatch and remove it. You’ll then be able to see exactly what this all looks like. It’d be better than experimenting with your lovely jacket.
The only other thing I can think to do is to leave the hood as is and change the placement of the embroidery so that it frames the face, even if the hood sts are going in the wrong direction.