Hmm, the stretchy bind off methods would be expected to resolve the problem. Some people find these bind offs add so much stretch that they do them with a smaller needle to counter some of the stretch and give a neater finish or reduced flare.
Have you tried binding off with a larger needle? Depending what I’m making I might go up 1mm or 2mm (or even more) in needle size for the bind off and do a regular bind off. Initially it looks a bit messy as it’s worked because the stitches are bigger making it look a bit loopy as I’m doing it. But I just trust in it and keep going. At the end I give the fabric a stretch and all the stitches even out and kind of bed in to the edge.
Perhaps knit up a swatch so you don’t over work the yarn on your sweater and try out a much bigger needle, you can also combine larger needle and stretchy bind off method to see how it goes.
Mostly I would recommend not over tightening the stitches as you bind off. It can be so tempting to tidy up the yarn loops but try it on the swatch, just letting it have the full size of the needle for each stitch and not tightening anything.