I can scan the router through the App and list the IP and mac addresses of all connected devices. But the app of course cannot know in advance the IP address the router assigns to positively identify the field device.
Are there any benign queries that you can send to the device, eg, retrieve firmware version, serial number, model number, perform a reading? If you get a valid response, then it is probably your device.
Or, have you decided upon a random (non-standard) port number for your device to communicate through? If so, then just getting any response on that port will filter out most other devices and thus increase the likelihood of this device being one of yours. Although some firewalls get a bit narky about non-standard port numbers, so that might be opening a new can of worms :-/
It sounded like you might be querying the router for a list of attached devices. This won't work on every router. Two other approaches are:
1/ transmit a broadcast packet (usually IP address 0.0.0.0 or 255.255.255.255) to which your device can respond with "here I am" (or perhaps: "here weIare"...)
2/ scan through the other 253 addresses (excluding x.x.x.0, the router address and your address) and see if you can get a valid response from your device