CfB's argument is the payee has an incentive to resubmit it with new PoW. (and so the PoW can't be signed by the payee)
Ahhh, yes, I'd forgotten about that; to some degree, that does mitigate the payer having to be online at all times, since the recipient (I'm switching to clearer terminology than 'payee') can always resubmit the transaction after redoing the work.
However, I'd like to discuss whether there is another way to approach all of this (not related to Iota), such that the payer does sign the POW which rules out pooled mining, while being totally different to your design, TPTB_need_war.
It all relies upon one critical point, which was a huge point of contention in our previous discussion: in a linear chain of transactions (A to Z), where B must point back to A, why must the transactions after A get orphaned if A is a double spend?
e.g.
A<-B<-A*<-C<-D
A* is the double spend. Why must C and D get orphaned?
If we can get over this point, I'll describe the entire idea.