The British Navy did indeed procure cheese, which was rather hard (but durable) and presumably became harder with age.
Knowing that cheese can go rather hard if dried out, I decided to test the cheese-button anecdote.
I used a selection-bag of cheeses:
Austrian Smoked Processed Cheese
cheese, water, butter, milk protein, emulsifying salt (polyphosphate), potato starch, salt, liquid smoke
milk, salt, starter culture, colour (carotene), preservative (sodium nitrate, calcium chloride), animal rennet
milk and cream, garlic and herbs (1.6%), salt, pepper
Mini Babybel Original
milk, salt, milk ferments, vegetarian rennet
Mini Babybel Cheddar Variety
cheddar cheese (94%), water, preservative (nisin)
milk, cheese culture, salt, rennet, colour (annatto)
Step 1: Preparation
The width of the strip was the only consistent accurate measurement, and would serve as a shrinkage point of reference.
The Boursin being mushy couldn't be cut, so it was spread onto a strip of plastic pizza-base.