I worked out the equations for landing and determined the optimal fuel to be 54%.

Some calculations (and a screenshot getting the perfect score!) at https://gist.github.com/sbliven/e5eacef1df5f64e820abf3c0be597c46

The trick is (spoiler -> base64)
dG8gd2FpdCBhcyBsb25nIGFzIHBvc3NpYmxlLCBhbmQgdGhlbiB0byBpZ25pdGUgdGhlIGVuZ2luZXMgd2hlbiAzMzYuNTggbSBhYm92ZSB0aGUgc3VyZmFjZSAoZ29pbmcgNDQuMzggbS9zKS4=