That is a cute little shrug. I read through all the pattern trying to figure out how it was made and it seems like that front panel-like area on each side of the front opening is what you are trying to do right now. Is that right? You work it up one side and back down the other to the other tie? I made a little tiny sample piece of the shrug and a tie and then picked up stitches along it and tried picking the stitches up along the front and knitting it together with the "panel" I was making of ribbing where it would be up the front of the shrug.
I don't know how it is supposed to be done, but here is what I did and it seems to look pretty good. I had mine set up so that on a wrong side row when I come up to the edge of the front where I need to join to the front, the last stitch I have is a purl stitch on the WS. Then I turn to the right side and I am presented with a knit stitch as the first stitch on the return row. All the stitches are on the LH needle and the spot I need to join is just to the right. Keeping the yarn to the back, I just picked up the left leg of the first stitch along the edge (from the back) with the tip of the LH needle. Then I just inserted the RH needle into what had been the first stitch on the LH needle and the leg loop and knit them together, like any K2tog. That joined the ribbed band to the front edge. Then I just kept ribbing across the "tie", turned and worked back and did it again when the RS was facing me next. I think to do it this way you need to be sure that you are really only picking up every other stitch along that edge. If you pick up each one, I think it would get too crowed and cause it to ruffle up.
Someone who really knows what you should do will laugh at my idea, but it works and doesn't look bad. Maybe if doesn't look right to you either, it will give you another idea.
If the first stitch facing you on the RS right where you need to join is a purl, you can pick up the stitch the same way I said above and purl the leg and the first stitch together. That looks pretty good, maybe even better. Good luck.