The proposer/builder separation, namely the Idea 1 outlined in this post introduces a ternary fork choice rule which in addition has the following status Block proposal present but bundle body absent. IMO, this new status can be perfectly combined with this proposal as it helps to get rid of the complexity related to transaction verification. Malformed block body may be deemed absent.
Moreover, gossiping the block body after the beacon block has been gossiped and received by the builder introduces an additional delay which may affect attesters’ votes. Having additional time for executing the payload will help to mitigate this issue.