Thanks for this interesting idea! Here is my concern.
Conjecture: this difference does not actually matter much in real life
I think the “modified GHOST” require a larger threshold for clique oracle (and hence it takes a longer time to finality) than the “regular GHOST” because the modified LMD GHOST is only “majority driven” i.e. a block need to be supported by more than the majority to be finalized.
For a majority driven fork-choice, the threshold of the ratio of a clique to the validator sets (by weight) is 1/2 + t - e where t is the equivocation fault threshold and e is the ratio of the observed equivocating validators.
For plausible liveness, t need to be lower than 1/4.
The “regular GHOST” is “max driven” i.e. the greatest set of validators agreeing on a block is sufficient for the block to be finalized. In this case, the threshold of a clique is 1/2 + t/2 - e and for plausible liveness t < 1/3.
(The original definitions of “majority driven” and “max driven” are introduced by Nate in the draft of section 7 of the CBC paper. The compiled version is here.)