What I would like to see is formal proofs of security for proposed specifications like this, covering security in fundamental properties, e.g.: “consistency and liveness in an asynchronous network with adversarial delays that are a-priori bounded, within a formal model allowing for adaptive corruption and spawning of new players, assuming that the computational puzzle is modeled as a random oracle.” This paper already proves that Nakamoto consensus blockchains already have these properties, and whatever changes we make should still have these properties. (With Casper, the part about the computational puzzle is not applicable, but the proposal mechanism should still be as random as practical or pseudorandom. Additionally there should be an analysis of security with synchronous cases such as cross-shard synchronous contract calls and internally synchronous zones.) Also do an analysis of the tendency towards centralization vs decentralization would be good, as well as whether there are asymmetries (particularly economic ones) between participants (e.g. like this analysis: Exploring the proposer/collator split), which can lead to a different Nash equilibrium than the intended one. Additionally assess whether there are externalities, which should be internalized for sustainability.
Then again, if you are just going to have a testnet without execution, then these research topics are less important.