The only issue is that I can't seem to connect to the wireless router to configure anything; I had to reset it to make this work after having changed the IP address before, so now http://192.168.0.1/ brings up the config page for the old wired router, where originally it had been defaulting to bringing up the new one.
Maybe if I plug it back into the internet port and change it, then go back to this configuration?
Yup, I’d expect that to work (probably with a power-cycle before trying to connect).
Also, most likely what’s going on is that the wireless router has gotten a random LAN IP address from the wired router and is using it, so you could try going to http://192.168.0.2/, ...0.3/, ...0.4/, and so on, and see if one of those is the wireless router. (You can skip any IP addresses that you know to be other things, e.g., the current IP address of your desktop computer and your iPhone.) But if you don’t find it quickly, what you suggest will probably work. (And it shouldn't be necessary to plug anything into the wireless router except the laptop or desktop you're trying to configure it from.)
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Also, most likely what’s going on is that the wireless router has gotten a random LAN IP address from the wired router and is using it, so you could try going to http://192.168.0.2/, ...0.3/, ...0.4/, and so on, and see if one of those is the wireless router. (You can skip any IP addresses that you know to be other things, e.g., the current IP address of your desktop computer and your iPhone.) But if you don’t find it quickly, what you suggest will probably work. (And it shouldn't be necessary to plug anything into the wireless router except the laptop or desktop you're trying to configure it from.)
Good luck!