The AP-365-RW should come with Instant firmware (or Unified firmware for early production models). If the AP has been converted to controller firmware, you can factory reset it to get back to IAP/Unified boot. From there make sure the AP is upgraded to the same version that your cluster is running on. As that version is below 6.5.2, first upgrade the existing cluster to a version that supports all different APs (AP-365 requires 6.5.2 or up as mentioned in an earlier response).
If you add the AP to the existing cluster, the new AP will not even come up because of an incompatible software version conflict. So it can be that that is the reason you can't see your new 365.
Cluster with 207, 305, 315 and 365 should work. I would upgrade to 6.5.4.8 (if you need a Conservative release) or 8.3.0.3. If you don't have a support contract, check what version the 'Check Version' comes up with.