Chase will typically post a temporary credit, but it has to give the vendor 30 days in which to respond. On the facts as you list them, it seems clear that you were entitled to cancel for a refund under FI's policy, but that G-T-G did not honor its own terms, e.g. applying FI's policy. This does not mean that G-T-G will admit this and thus there is no way to predict the outcome.

It all comes down to risk tolerance. If you do not want to take the risk, then accept the existing ticket (and make certain that you withdraw the chargeback as well as speak directly with both G-T-G and FI). If not, then let the chargeback play out and purchase the new ticket, understanding that you may wind up with two tickets.