Proposal: Protocol level rotation between PoW and PoS blocks with separate difficulties. Example Block A is found under bitcoins current PoW system with a difficulty of ~12billion (difficulty A) in a majority ASIC mining environment. Block B will then be found under a PoS environment that requires the coin-age of the blockfinder to be included and consumed in the block. Block B would be subject to a separate difficulty B such that a combined effort of CPU mining and coin-age (say difficulty / coin-age or difficulty to the coin-age root) could also be adjusted to similar 5 or 10 minute intervals.
How it fixes problem in PoW: 51% are based on the knowledge that the attacking party will eventually be able to control all blocks that are added to the blockchain. Interjecting a separate PoS system between blocks makes this impossible. At the same time, it frees PoW miners to work in their best interest and capture even upto 100% of the mining pool distribution.
How it fixes the problem in PoS: So called nothing-at-stake attacks are based on the assumption that any self-interested minter would continue to mint all forks of the chain in an effort to maximize his potential rewards (due to very low cost of minting). To the limit of such a case, all branches of the blockchain are continuously mined, and no single version is provably authentic. Interjecting a separate PoW system between blocks provides the resource intensive requirement to prevent the blockchain from spiraling out of control.
Side-thoughts
part of the original reason for PoS was to avoid the electricity cost of PoW. PoW miners could be setup to run on standby (only listening to the network communication) after a PoW block was found. Upon communication of a PoS block, they would again run at full speed. That savings vs. costs of thermal cycling or lost mining time could be optimized per mining hardware.
- block times could be modified for 5 minute averages (5 mins PoW + 5mins PoS = 10 minute overall) so that PoW rewards stay consistent during the cutover.
- As mentioned, a hard-fork or side chains using "burned" coins could be used for implementation