No idea how high you’d have to be, but here are some suggestions for alternative ways of getting the orthographic image you want which won’t require being on top of a ladder or a skyscraper.
I’d use Reality Capture photogrammetry. Once you have the 3D model of the subject, you can then get an orthographic view. Accuracy should certainly be better than 2mm. This video explains how to get an orthographic view from Reality Capture.
https://youtu.be/VFYuLfTUG1M?si=JinApjjfU0kcmCit.
There’s a small charge for processed scans - probably a few pennies. Alternatively you could use Reality Scan photogrammetry for free and then import to Blender and get an ortho image that way. Photogrammetry involves taking lots of photos of the subject to generate a point cloud, but you don’t have to be far from it or worry about distortion. It also saves needing to do deskewing.
If you can borrow a 3D scanner with colour capture that can be handheld, that would give the best accuracy and would be a better option than photogrammetry.
Lightroom can correct perspective distortion and might possibly be able to modify the image to an orthographic view. Deskew first. Also lay a grid over the subject so that you have a reference photo to check settings against. 3D scanning with scanner or photogrammetry will probably be easier and give more accurate results.
If using 3D scanning, then depending on the subject, if it has large areas with no features, it will help to put down some marker dots (or cut up blue masking tape into smallish pieces).
Others may have better suggestions.
ETA - if the pattern is on 2mx2m paper, then you could also scan it in sections using a book scanner (the lid folds fully back). But if the sheet is stiff, that’s not going to work because of the raised control panel. Happy to lend mine in return for a donation to the space if you can collect and return it to Holloway.
