I tried to carve the bitcoin logo with a knife, it always failed because the cheddar cheese was so soft and brittle, I wasn't good enough to see it.

Imho, cheddar is not the best solution for bitcoin pizza due its high fat percentage meaning it can't handle the oven heat good and will melt very fast.
I've been making bitcoin themed pizza for years and experimented with all sort of cheeses; from cheddar, gouda, ementaler, harvati, edam, milner and many others to even halloumi which is known for its resistance to heat (thats why its usually grilled), but imho taste doesn't fit pizza good).
Through trial and error I realized that Milner showed the best results as it was a yellow cheese that generally goes well on pizza, and most importantly its not too fat, meaning it can handle oven heat (up to 200 degrees for 7-8 minutes) while keeping consistency so for the next year bakeoff I suggest you to try with that one.
Few examples from previous years, done with milner cheese.
