i see two problems here.
If the txn included isn't known by all nodes then it will have to be relayed directly and that increases block propagation time and orphan cost.
as you stated a miner does not know which transactions are known by other nodes. so he does not have a choice: he must publish all transactions in his block.
and if i understand you correctly he must do this fast (a priori?) otherwise he risks an orphan (because other miners cant build upon his block).
^ if that is true all is fine: but thats definitely not O(1).
A miner has no way to of knowing if all nodes contain all transactions as if the txn volume exceeds the bandwidth availability or other resources of a given node then it will drop some transactions.
if - because of bandwith - not all transactions reach a node the node cant decide which one to take. maybe an upstream proxy could be developed but that sounds a little strange to me.
it gets worse, because different parts of the network will see and keep different transactions.
did i misunderstand you?