4 billion yen to save the whole kingdom sounds pretty cheap. Even if they're cash-poor, the king could have thrown in stuff like hereditary nobility or something, rather than the vague "you'll have preferential treatment".
Even after many rereads, of the LN and manga, I don't know why Ferdinand cares about erasing evidence. For one thing, the actually important witnesses (Toad and High Bishop) are still alive and well. For another, it's evidence of his enemies' crimes. Why erase it?