My design doesn't (and afaics shouldn't need to) prove to a syncing node anything about propagation that occurred while that node wasn't listening live. Remember that the 49 - 99% attack must be sustained otherwise it can't maintain the blacklist on the minority PoW. The minority PoW will have identified the dishonest chain and be humming along (at a reduced level of PoW difficulty, yet still including the attacker's nominations so as to prove to syncing nodes which chain is refusing to include the other's nominations). So the syncing node will have ample opportunities while live to objectively determine which chain is dishonest.