I can confirm that this solves the sideloading issue for devices that are able to skip setup, but am unable to test on a device stuck at setup as I don't have one in such a condition. Thanks to Leo and then TT for finalizing and putting together the steps.
Please read and follow each step meticulously;
NOTE: If you are able to skip through setup; wait for the "Complete Setup" notification to appear, tap on it, then tap "Open" at the bottom of the screen. Tap "Next" to get to the "Connect to Mobile Network" screen and proceed to step 2 below.
1. Start up your device and proceed to the "Connect To A Mobile Network" screen.
2. Press the Power button of your device three times in quick succession. You will hear a short chime if successful. (You may need to try pressing the Power button three times and then tapping the screen quickly with two fingers.)
3. You will then see (and hear) a pop-up informing you the Screen Reader software has been turned on. Double-tap with two fingers to enable the software.
4. Tap, then double tap "Skip" on the cellular connection screen.
5. You will hear the Screen Reader start reading off comments about Blackberry ID, even though you will see the Wi-Fi setup screen that you've been stuck on for weeks. Wait until you heard the Screen Reader say "Skip" then IMMEDIATELY double tap the screen at the top left, right below the words "Connect to Wi-Fi".
6. You should see a pop-up allowing you to skip BBID creation. Tap, then double tap "Skip" again.
7. You will then go to the standard BBID sign-in screen. At this point you can turn Screen Reader off by pressing the power button three times in quick succession again.
8. Select "Skip" on the BBID screen.
9. If the Software Update screen appears, skip to step 10. If Regional Settings appears you will likely get an "Unable to Connect" error. If so:
Press the Settings button, then tap on the Wi-Fi network you're currently connected to, and tap on the network again once it's done loading to reconnect to it.
Tap the "Next" button at the bottom of the screen to go to the Regional Update screen, and "Next" again immediately after it appears and it will take you to the Software Update screen. You may need to run through these two steps a few times to get past the error.
10. Software update will take a VERY long time but will eventually tell you it can't connect to Blackberry infrastructure and offer you the option to swipe left or set up Wi-Fi. SWIPE LEFT! (We don't want to go back to that Wi-Fi screen....)
11. You'll then see an Automatic Updates notification; tap OK.
12. You will then be taken to the standard gesture tutorials. Complete those and you're done! You will find you will be able to sideload normally and use any native BB10 app you want.
Here is also a visual guide that has surfaced;