However, time and hot water has distressed the jacket very nicely, so I thought I'd try and fix the sagging.
Solution? Textile glue.
I glued the cargo pockets and handwarmers shut. Then, I undid some stitches on the lining, reached inside and applied glue in an L-shape along the bottom and zipper side of the pocket.
I forgot to take a 'before' picture, but this is the 'after' shot:
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Which, believe me, is a vast improvement!