Baseband > 2.0.1700.48 won't work without proximity and light sensor working? I have the same circumstances as Nexus 4: Stuck on boot animation for baseband version != 2.0.1700.48 and android version > 4.3. I have repeated the first two sets of tests, with precisely the same result. I am currently running build JWR66Y (4.3) which comes with baseband 2.0.1701.0, which I have back-patched with the baseband from the previous release, 2.0.1700.48. Attempts to upgrade past 4.3 fail. 

The coincidence that stands out is that I, too, just had a screen repair done. Before my screen broke I was happily running 5.1. Even after the screen repair, with a broken proximity sensor in place, it still ran 5.1 just fine. The trouble happened with I returned to the tech who fixed the screen with a complaint about the proximity sensor. The tech insisted that he could not get the proximity sensor to work. We finally agreed that he could just leave it out. That lead to the current problem. 

So I wonder if the difference between baseband 2.0.1701.05 and 2.0.1700.48 is that 2.0.1701.05 checks for either the proximity sensor or the light sensor (they are on the same board) during startup, and hangs the boot  waiting for the sensor(s) to come ready. This idea could be tested by repeating the test before and after doing surgery on a working Nexus 4. That's a lot of work, and fortunately I can't do it myself (no working Nexus 4 proximity/light sensor board!). But maybe someone has relevant experience. 

If you look around on the net, you see lots of Nexus 4 problems relating to 4.3->4.4 upgrades failing, lots of Nexus 4 problems relating to the proximity sensor breaking after screen replacement, and several apps that do nothing but disable broken proximity detectors. There also hints that the exact placement of the rubber grommet separating the proximity and light sensors from the front glass is critical. 

The reason my question is interesting is that I could go back to the tech and ask him to replace the proximity sensor (so the thing boots in 5.1) and hopefully adjust the sensor grommet (so the proximity sensor works). Even if the proximity sensor never works again, I could still use one of the software solutions that disables the proximity sensor.
I have good news.  My tech put the sensor card back in my Nexus 4, reversing the rubber grommet that separates the sensors from the front glass.  The promity and light sensors then both worked, booting from 4.2.2.

I then used the stock image of 5.1 from https://developers.google.com/android/nexus/images to update the phone to the latest L release.

Everything works.  I take this as good evidence in favor the hypothesis that the absence of the sensor board was causing the boot loops described here and in the earlier article.