The best solution is to just use a simple gps app on phone that will record a log file. this will typically be a .gpx file. You can them import the gpx file into lightroom and sync the gps coordinates based on time. (So, you do want to update the clock in the camera to accurate time and you just need to know the time zone offset during import. I have used gps trackers on my phone while on backpack trips without charging the phone. (Only used gps app while hiking 4-5 hrs for 2 days)
Pretty easy solution and does not waste any camera batty capacity while in the field.
I'm pretty familiar with this approach and have used it in Lightroom for years - one of the main reasons I use Lightroom actually (the map module) but I use an actual GPS device and not my phone. I don't know if that's the "best solution" though. The best solution for what?
I haven't seen any major difference in battery life keeping the Bluetooth turned on on the camera. I'm sure there is some difference, but it really doesn't seem to be that bad. Also, there's an option to sync the camera time with the phone time when you connect the app which I find super handy and haven't had to do any time offset syncing the pictures. I use my phone as the remote control for my camera quite a bit, so why not transfer the coordinates while you already have the phone connected?
Based on your example, how do you get the coordinates for the pictures you took while you were not hiking (outside of the 4-5 hours)?
As I mentioned, the app also has the ability to log the GPS coordinates even if the camera doesn't have Bluetooth on. This functionality doesn't work with my camera but will probably work with a higher-end camera like the R5.