There is never a consensus on the burn base fee floor (in any of the designs), and it is not necessary. Each attester simply rejects any block below their subjective floor.
No verification is needed.
The honest proposer selects the block with the highest burn base fee floor and has 2 seconds of safety margin. If there is a block with a higher floor that they may miss, just around the start of the new slot (D+2), then the majority of attesters will not enforce such a floor. This is the point of the original design and remains the same. Thus, no substantial uncertainty exists if proposers play it safe. It is correct that if proposers do not play it safe, then they may miss their block and all rewards. Let’s review the game mechanics.
Builders are incentivized to win the auction at the observation deadline by providing as a high payload base fee as possible (the part that will be burned). Before this change, no such incentive existed, which is why we suspected a lower base fee floor. A short time after the deadline, some builders may focus on raising the payload tip, if they believe that proposers will select based on the payload tip. This is true also in the vanilla design, but there builders may opt for this strategy also before the observation deadline (if they bid at all). A realistic outcome (in both versions) is thus that both proposers and builders focus on raised payload tips after the observation deadline. Since a higher payload base fee under competition will lead to a lower payload tip, both parties are incentive-aligned as such. Builders will likely keep track of any raise to the payload base fee also after the deadline and make a probabilistic judgment on whether they need to match it. The decision will depend on if the raise happens at D+0.05 (proposers may wish to play it safe and treat it as the floor) or D+1.9 (proposer may be more confident, and not treat it as a floor that will be enforced). The decision will thus evolve with proposers’ behavior.
Some builders may target unsophisticated proposers by raising the payload base fee after the deadline and some may target sophisticated proposers by raising the payload tip. Some may run both strategies in parallel. Note that it is not possible to remove the payload tip, as it prevents giving an edge to proposers and builders that settle out-of-band after the observation deadline.
If there is substantial MEV but the payload base fee floor is very low around the observation deadline, a builder that wishes to cause consensus instability may provide a bid just at the deadline that makes it impossible to match when providing any relevant payload tip, and hope that the proposer gambles by ignoring it. Thus it is not a flurry of bids per se that is the risk, but rather that the bids just at the deadline differ substantially from the bid before the deadline. The vanilla design will be susceptible to such an “attack”, but on the other hand it does not provide any incentives for bidding just around the deadline at all.
The change will give builders an incentive to provide bids that are within the deadline so that they win the auction. There would in that way be less possibility for an “attack” that seeks to cause consensus instability. However, there are scenarios where builders strategically wait to provide bids until just around the deadline. If this is a concern (and it does seem pretty valid!), the deadline for selecting the subjective winner could be shifted to be slightly before the deadline for selecting the subjective base fee floor. The proposer will then always select a bid that at least matches the winner of the auction and not gamble. It will then also not be possible for an attacking builder to subject the proposer to substantial opportunity costs by bidding when attesters set the base fee floor, without also taking on an expected loss.