Try just knitting three stitches with old and new strand together, so the ends point in opposite directions. Knit those three stitches tightly, to reduce the bulk. Leave a 1/4" tail on the "inside" of the garment, if there is one, to keep the ends from popping out to the outside. If there is no inside of the garment, see if you can leave over an 1/8" tail to keep the ends in place; they should be pretty hidden with chenille.
KnittingHelp Queen Bee
"There is a vitality, a life force, an energy, a quickening that is translated through you into action, and because there is only one of you in all of time, this expression is unique. And if you block it, it will never exist through any other medium and it will be lost. The world will not have it. It is not your business to determine how good it is nor how valuable nor how it compares with other expressions. It is your business to keep it yours clearly and directly, to keep the channel open. You do not even have to believe in yourself or your work. You have to keep yourself open and aware to the urges that motivate you. Keep the channel open."
— Martha Graham