I am not sure how the sybil attack would work in this scenario. I would have thought the lottery system would attract a large number of cheap nodes. An attacker would find it difficult to get a useful proportion of nodes into the system to allow them to influence the network.
And so, what is a node?
A private key?
An IP address?
?
A port?
https://www.reddit.com/r/Bitcoin/comments/2vv8m6/pseudonode_when_is_a_full_node_a_full_node/One would have to wonder what would happen in this model if you introduced a proof of stake. E.g., each node must own 1 coin -- max coins being 22 million.
I would do multi-sig to ensure that the node could sign the proof with one sig but require two sigs to transact, protecting it from hacking.