EDIT: I found a solution! Not exactly by anoyone's suggestion, but in the end I did as follows: I selected the whole object and applied the 'UWV Map' modifier to it (making sure my world units/unit setup was 1 unit=1cm and that the model was the correct size). I ticked 'real-world scale' in the 'scale' part of the sidebar, and set the unwrap projection type to 'plane' (this didn't really matter since I was going to manually unwrap it anyway). I collapsed that modifier and applied a 'Unwrap UWV' modifier. I then scaled the whole UWV island down to 1% of its original size (enter 1 in the scale box and make sure you're maintaining aspect ratio between x y and z) so that it would fit in the UV tile (which was equal to 1cm). I unwrapped the object as normal (in a way which would work best when sewing the object IRL), but only using the 'quick peel', 'relax until flat', and 'stitch' options (with 'avoid overlap' turned off in quick peel settings) so that none of the islands would change size, just shape. Finally, I arranged everything and exported it onto a 1024x1024 png.
I took it into my editing program (Clip Studio Paint, but you could use Photoshop or whatever), and changed the DPI of the image to '300'. 3ds Max exports at 72 DPI, so setting the DPI to 300 scales the image back up to the correct 'real life' size.