Your work is not a non-existence proof, it's an analysis of a specific scheme. You made the same error in reasoning in your prior orphaning work, where you erroneously concluded that orphaning was proportional to the size of the block-- this later work implicitly admits the error by saying it is proportional not to size but to the rate of additions, but does not go far enough.

You proposed a needlessly deficient design, one which was inferior to what I'd already described to you, due to having the flaw of increasing orphaning risk to add new transactions.

This flaw can be simply (and compatibility with your design!) corrected by miners: in your scheme miners add transactions by adding them to a block attempt, thus taking orphaning risk.  Instead, miners could add transactions by first adding then to a separate hash tree, committed to by the block whos data is only shared with weak blocks, not full block solutions.  Only when a transaction is well and buried in this second tree, do miners then add it to their blocks.  Avoiding the orphaning risk resulting from doing so.

Not only can miners do this this mitigate the orphaning from the new addition, but you cannot prevent them from doing so.