The maths seem to be correct though when I enter it into archery calculator I am getting quite a bit lower joules so I'll have to double check if there is an error in your maths or how I am using the calculator.

A few issues with assumptions on the inputs is my main critique. Firstly 10 degrees is fairly shallow but most important the assumption of only 5 joules lost energy per 10 meters. That is probably about right for modern vaned arrows but all the tests I've seen on authentically feathered longbow arrows have quite a bit more slowing due to the much higher drag. Also 64 gram arrows at 63 meters per second is a bit high. Not outside the realm of possibility but would probably require 180+ lb draw and that is the upper range of weight for the arrow and getting close to the best case scenario especially considering slightly pulled release will greatly affect results at any range past 40 meters which for most battles that English archers participated in would be just a bit beyond point blank range.

The final issue is something I'm not sure of the maths behind but angle of impact doesn't quite describe hitting a rounded surface vs a flat angled surface with a broad point that is likely to be off straight hit both by vertical and horizontal axis.

I do believe some arrows could penetrate lower quality plate but mostly at closer ranges and even then not reliably though if several bowmen aim at the same person some arrow could probably be effective enough to kill at ranges less than 20 meters. Descriptions of Agincourt mention 800 men at arms approaching on foot and wearing presumably poor quality plate making it to within 60 yards of the English before significant casualties and around 200 men closed to melee. The other 600 are described as wounded or dying but losing 600 men crossing only 60 yards is severe casualties. However they were thrown into disorder by the retreat of some French cavalry, coming up a slight hill over very muddy ground. Even if trying to move fast probably were close to a normal walking pace and would take 40-60 seconds to cross that distance giving the English 4-5 volleys from a couple thousand archers or roughly 10,000 arrows vs 800 men.