One approach I've found helpful might be seen as "between" 4 and 5 - Go back to the drawing board (communicate a better solution more persuasively) by Going out to the masses, but with the twist of the "masses" being other folks who have solved a similar problem. By finding and showing the stubborn client examples of others "like them" who have solved a similar problem, you
a) Keep your persuasion points positive and focused on their success
b) Eliminate the "my solution vs. your solution" confrontation
c) Help them lower fear of risk by hearing other's success stories (you can also try
fear-of-failure stories, but for some reason it's harder to find supporting blogs/white papers about failures, and citing only your own opinion, well... see point b.)
d) Demonstrate a honest effort to solve the problem (like ptailor129 suggests.)
Even if this client fails to "do the right thing", you gain knowledge for the next round by performing at least a quick review of other's solutions....and who knows, while digging, you might even discover something better which neither of you considered.
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