Well, if you are willing to pay a bit of interest, it would be interesting to find out. You might be the first person here to actually use Pay Over Time, and with no other revolvers, yours would truly be a pristine experiment. The APR on those POT is quite painful to imagine.
To pull it off, you would need to get enough charged up to trigger the POT option, then let it report on a statement or two, and also pull a credit report after those statements reported to verify how it works.
On the other hand, the Credit Union card would definitely report as revolving, and probably have a lower interest rate (and you would not have to pay interest to find out, it would be a revolver just with the grace period reporting).
As it is now, with only the AMEX Gold charge card, you don't report any revolvers, and that is probably hurting your score.
Regardless if you decide to test POT (and become a living legend here) you will want to definitely get a specific revolver credit card to have that report a non-interest charging amount on the statement to improve your credit score.