Apparently there's a way to add a carabiner to a Garmin GPS device. I wonder if there's a way to hang it somewhere close to the window whether flying Y or J?

I can confirm this. I routinely use GPS apps while hiking in areas with no cell service. I have also once tried a phone with no SIM installed and using a radio relay--the GPS part of it worked, under the conditions the radio range turned out to be too short to be of much use for what I was after. (It provided a text version of a walkie talkie, but used your phone as the interface.)

In my experience GPS locks on planes can be hard especially if your phone's aGPS data hasn't been refreshed recently. IF you just got a clear ground lock before take-off, you should be able to establish a lock mid-air reasonably easily. If that doesn't happen, hold it to the window for a good 5-10 minutes. On B737s and A320s I've had no issues.

On 787s... that's a totally different story. Cell signals struggle with 787s whether I'm in Japan, China or the US. I haven't tried GPS independently because by the time I think about it I remember how I should refresh my aGPS by opening GPS Status but by then I lack network connectivity. But then again I mostly fly on J for 787 routes so usually I'll just enjoy my PDB or just start playing some music to cure my boredom rather than worry about GPS.

Fairly certain no phone actually needs a cellular network to lock. The GPS has always been independent of network, but the assisted portion may help download GPS data for a faster lock. The problem with many older phones, especially back when Google Maps didn't have an offline option was they just wouldn't load the map, but a standalone GPS app like Android phones have had would be able to confirm you have a GPS lock and display coordinates.

A typical GPS receiver, either in a phone or a stand alone unit will get a lock more quickly if you have not moved appreciably since your last fix. This is due to a roadmap of the satellites called an "Ephemeris" being constantly downloaded from the system. Among other things it contains info for the satellites that should be available and their approximate positions. When you change locations before a power up, the old map is no longer accurate, and the device must start from scratch, so to speak. Add to this the fewer sats visible through your window and the difficulty is compounded. My iPhones keep GPS active in Airplane Mode, so I would recommend obtaining a fix before taking off and try and keep a fix the whole trip if it might be desired.