Yes, I think you can use kitchener stitch to solve this problem. I have not done it myself, but I have this to offer from Elizabeth Zimmermann's book Knitting Without Tears
. Great book!
She had spoken of correcting an error in a cable that was at the beginning of a sweater that was almost finished. She had done it by lowering the problem stitches and doing them back up with a crochet hook. Then she says, "I wouldn't take this trouble any more, by the way, but would snip one stitch a couple of rows above the error, let down the stitches, correct the error, knit the stitches up again, and then weave the snipped row back in. I am truly boss of my knitting. I would also eliminate an indelible stain this way, if it wasn't too big, by extracting the offending rows, one at a time." Page 42
If she could do this to take out a stain it could also be used to fix a hole. When she says "knit the stitches up again", I think she means with a crochet hook. And where she says, "then weave the snipped row back in", I think she is referring to using the Kitchener stitch.
With a diligent search you might find someone who has done this somewhere on the internet. Maybe a blog. If you can't find any help make a swatch and try it out. Maybe with a little experimentation you can figure it out. I have a friend here in my town that I bet can do it.
She is a knitting genius. If you get desperate, e-mail me and maybe I can learn how to do it from her and pass it on to you.
I've always thought I should learn to do that, but never have.