That sounds like it'd require a custom read head. Normally, a floppy read head is comparatively small, and has to be moved across the disk's radius with a step

That sounds like it'd require a custom read head. Normally, a floppy read head is comparatively small, and has to be moved across the disk's radius with a stepper motor. To read it in one pass would require a head that can read all the tracks at once, so this would be something specially-fabricated, which doesn't sound cheap at all. I'm sure it could be done (esp. considering how old floppy tech is), but I don't think it's something you're going to just fabricate in a small lab with spare parts, it'd need something custom manufactured.