the screenshots here were hosted on imgur and are now gone. I'm sorry and I have learnt my lesson about relying on third party media hosting.
If we have a network where most of our devices (including our own computer) exist in the 192.168.1.x IP range, and we have a device which is inaccessible due to existing in a different IP range (192.168.10.x), we can change our own IP to be in the same range as the lost device, edit the lost device's IP address from there, then change our own back so that now all devices on the network exist in the same range and are all visible to each other. If our default gateway has a 192.168.1.x IP address (it probably does in this case), then we will not have an internet connection on our computer while we're visiting 192.168.10.x to retrieve the lost device. This is to be expected.
If we know the assigned IP address of the lost device, all we need to do is join the IP address range where it is, and we should be able to connect to it directly by entering it's IP address in a browser, or however else this device takes configuration connections. To change our own Windows machine's IP address, we right click the network icon in the system tray and select "Open Network and Internet Settings"
Then from that window select "Change adapter options". This should show us a list of the available network adapters on our system. Right click the active one (for me that's Ethernet 2, this will vary), then open "Properties".
In the Properties dialogue, look for "Internet Protocol Version 4" in the list of items, select it, and click the "Properties" button. Here we can manually set our own IP address, or set it to be assigned automatically by the router/DHCP server.
Select "Use the following IP address:", and use settings as above except for "IP address", which you should set to something arbitrary in the 192.168.10.x range (assuming that's where your lost device is). Once you've applied these settings (ignoring any warnings that your default gateway is on a different subnet to you) you should be able to access the lost device's web interface, set it's IP address to something in the 1 range (or preferably set it to acquire an IP automatically from the DHCP server), then apply those settings. If you can no longer reach the device from your 192.168.10.x IP address, you did this correctly and the device should now be visible from the rest of the network. Set your IP back to 1.x/automatic and all should be well. If the device remains lost, you can use a tool like https://angryip.org/ to give you a list of the devices on the network and their IP addresses, which can help you locate anything missing. Bear in mind that you can only see devices on the same subnet/IP range as you.
(I tried to make this guide as general as possible, but in the case of the NAS we're talking about, the IP is 192.168.10.220 currently, and it needs to be changed to have a default gateway/DHCP server of 192.168.1.1 and to use DHCP to get its new IP address. These settings should all be accessible through its web interface.)