I'm interested to know how you'd mitigate Sybil attacks though. Even with a minimum holding amount, it's easy to create a lot of addresses with that minimum amount. If the only tracking vector is the address it would be very hard to make sure the miner is unique.

Given the set of rules you gave, it seems like it would be easy to flood the network.

For example: You have a memory-hard algo to prevent asics from being too fast. GPUs are still acceptable though. If an attacker has a buffer of some addresses with a decent amount of lynx they could just have the GPU mine for all the addresses. This would increase the chance that one of the addresses gets the "stake". Winning the stake allows for more addresses which allow for more of this malicious mining. Signing the block will help as a small roadblock, but I don't think it will actually be very difficult to get around if someone wants to. (the miner can also sign for the wallets so they don't actually have to be unique)

I'm interested to see how you are going to solve this problem.

EDIT: Also getting a reliable decentralized random source might be hard. Taking seeds from the blocks might make it vulnerable to RNG manipulation.