I think you need to look at the "local" modes when it comes to setting up your own dhcp-server on the IAP.
https://www.arubanetworks.com/techdocs/Instant_86_WebHelp/Content/instant-ug/dhcp-conf/local-dhcp-sco.htm?Highlight=dhcp%20serverusing "Local" - the clients connected to that subnet will be (source)natted to the IAP-IPaddress, the AP will get when getting connected via the wifi-uplink.(-> NAT forwarding mode).
using "local,L2" is dependend on the functionaly/limitations of the network you want to connect to - will it allow multiple MAC@ from a single connected client (as your IAP is a client in your setup). If multiple MAC@ do work, you do need to know the def-gw address (can be seen on the IAP when it is connected) and avoid "duplicate IP addresses". This is the setup where the default-gw is not the IAP itself.
using "local,L3" might be also an option, if you do make sure the IAP will always get the same Address when connecting to the WIFI-uplink, as you need to add a static route to that IP-address for this separate subnet used for clients connecting to the IAP.
hope this helps
Wifi client ~~~Test SSID~~~AP-303H ~~~~WiFi uplink~~~~AP-505H------wired------Internet router with DHCP-----Internet
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