Here is a really easy way to implement "proof of replication" in bitcoin:

Require each mining attempt to hash the last "n" blocks, instead of just the current block.

Here is a really easy way for bitcoin to democratize mining pools:

Instead of hashing attempts to find a golden nonce, require signing attempts, where the key used in signing is 1/100th of all the coinbase outputs.  This would mean mining pools realistically could only have around 100 miners each.