Unwrapping at an odd angle

I’ve been redoing the unwrapping of one of my creations to make it more texture friendly, however when I unwrap it, the UVs end up with a strange alignment (fig. a). Manually rotating it works to an extent, but is imprecise. Is there any to unwrap it so that upon unwrapping it looks more like (fig. b)? I’ve tried the various unwrap modes that you get by hitting the U key, but so far nothing’s helped.

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In Object Mode, press Ctrl-A to apply rotation to your mesh. See if that helps. IF not, try selecting just a few faces on the back of your mesh, use Project from View, Pin those few faces in the UV window and then do a full Unwrap.

Thank you, the second suggestion worked.