Holy Cow! You are impressive, sir. It certainly could be my Frank, but there are problems with that. Let me tell you what we think we know about him and why I see problems.
From Two consecutive census records we believe his birth year to be 1868, born in Ohio, almost certainly in Toledo, asserted to be "the baby" of the family of eight siblings born to John Albert Cooper and Catherine Bowers. He is also asserted to have been a painter in Arkansas around 1917, but I don't know how much credence that assumption might have. I did locate a Frank Cooper as a boarder, and listed as a painter in Arkansas in one census, but his birth year seemed off and he vanished in the following census anyway.
The connection you have found seems far more credible. But there are a couple of problems with it that may indicate a disconnect. I just looked up this family in the 1920 New Orleans census count, and this Frank's age puts his birth year at 1853. That's too early for my Frank even though some of his siblings did span that period. And he lists his birthplace as New York, which is another red flag that it is the wrong Frank, even though he seems to solidly link to the one you found in Toledo (New Orleans wife is Isabelle). I have no doubt that this is the Frank and "Isabella" you found in Toledo, but it seems a very long step to think of him as my Frank. While lying on a census form is pretty common, it is highly unusual to make yourself appear older than you are, and your place of origin offers very little reason to make up a new one unless you are hiding from the law. In 1920 this probably wouldn't be necessary even in that case.
With the magic you have displayed so far I have little doubt about your ability to pull yet another card out of your sleeve, but this hand doesn't seem to be a winner. I won't ask you to continue your search despite the knowledge that you seem to be able to produce miraculous results. I can't begin to thank you enough for what you have done. And you have definitely convinced me to start favoring those city directories, too!