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Put it in recovery mode while plugged into iTunes and leave it alone until it's done.
 
Perform another DFU restore to 9.2?

If you do a DFU restore today (after the 9.2 release), iTunes should download 9.2 as the version to install. DFU mode doesn't care about what's currently on the phone, so you can go ahead and just leave the phone in DFU mode until iTunes does its restoring. If you unplugged while it was restoring, it's possible that iTunes didn't get a chance to transfer over the whole firmware. iOS itself isn't something that can be wi-fi synced to the phone after the lightning connector is removed.

EDIT: I'm assuming you mean something like this when you mention DFU:
 
I plugged it in to my computer via USB, performed a hard reset, and the iTunes logo popped up. Maybe that isn't DFU after all?

Strange thing is that my phone works, even after I unplugged it while restoring. So is it best if I restore with this DFU mode as opposed to regular iTunes? Do I only need to do it once? Is DFU mode better overall if I want to clean install?

Thanks for the tips, btw.
Restoring half-cares about what you currently have on your phone. This is the mode that your phone uses when it updates. If the phone has an iTunes logo on it, it's launching in Recovery mode. This mode will let you restore your phone, but in some rare cases, it might re-use some of what was there before. This could cause iTunes to throw an error in some rare cases.

Device firmware update mode doesn't care about what is on the phone before you put it in that state. It bypasses the usual boot-loader and straight into the hardware DFU mode. It basically tells iTunes to ignore everything about the phone other than what it is (what model) and tells iTunes to just wipe everything out and re-flash the phone. This mode could also be used to install an older version of iOS if Apple is still signing that version.

The DFU mode is better if you think something is messed up or if you need to completely wipe out everything as everything will be replaced, and iTunes shouldn't throw any errors due to incorrect jailbroken drivers, etc because the device doesn't use the usual boot-loader to get into this state. The drawback is that DFU takes a bit better timing to get into, but the nice thing is that it's more sure-fire once you get there.
 
You just enter DFU mode as per the 40 second video above and make sure that your phone is plugged in and your iTunes is up to date. iTunes should see the phone and then ask to restore for you. If your phone times out on DFU mode, you might need to re-enter DFU mode, but iTunes should still continue its download and would be ready to go when the download is complete.
 
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