The one thing that this redesign does not address is decluttering. Your design has reduced space for the information that is needed, such as name and signature.
The original, despite being ‘ugly’, gives a large area for any writing style you may have, huge signatures and names such as “Guðbjartur Þjóstólfursson”.
It’s a tight brief — How can you design something that is accessible, easily understandable, gives you enough room for signatures and multi-syllable names, looks nice and is small enough to be posted through letterboxes and be compact enough that delivery drivers can carry 1000’s of them at a time without compromising space.
I would suggest revisiting fonts that lend themselves to tight spaces, yet optimise legibility, and perhaps trying a different layout. I would stick to the Open Box style of input, giving more freedom to writing styles / names etc