It doesn't seem likely that it would idle fine cold if you jumped time and not even start when the engine is at operating temp.
This might be electrical. Anything from a failing fuel pump to a faulty ECT sensor and everything in between.
But your computer is still setting the ckps circuit code after replacing the sensor and that can't be ignored so maybe look into why that's happening first.
When it gets hot and won't start, check for Spark on an ignition coil and a Ground signal to a fuel injector to rule out an issue with the ckps or camshaft position sensors and their circuits.
You wouldn't be the first guy that got burned by a ckps sensor code being caused by a faulty camshaft position sensor.
Those are both hall effect sensors and when they're failing they sometimes act up when they get hot.
Maybe that cam sensor is internally shorting to power and its signal is stuck on high voltage and instead of the computer setting a camshaft code it's blaming the crank sensor? (wouldn't be the 1st time that happened to somebody).
Here's a link to: https://troubleshootmyvehicle.com/Nissan-Index-of-Articles/Nissan-1.8L-Index-of-Articles/Page-1.html
Among the articles they have one that's a NO Start Case Study. Read over that one. There's another that walks you through testing for spark. There's one that walks you through testing the crankshaft position sensor wiring and signal. There's another that walks you through testing the camshaft position sensor wiring and its signal (on that one you might 1st want to use the starter to crank the engine to see if the voltage on the signal wire is stuck on either 10 volts (or 0 volts ((less likely with that timing advance you're seeing))) as you crank the engine before performing their test to check for an "on/off" voltage signal.
They specify that these tutorials are for a Sentra 1.8L from 2000 to 2002 but yours uses the same (3 wire) hall effect sensors for the crank and cam sensors. The wiring colors may or may not be the same. The wire positions on the connectors should be the same. Look that up for your 2006 on the internet. The spark test also applies to your COP coils.
Those tutorials for the sentra don't include how to test the Ground Signal from the PCM that triggers the fuel injectors but there's dozens of videos on the internet on how to do that with a test light.
These tests are easy and all you'll need is a cheap test light, multimeter, and HEI spark tester.
This would be a good starting place for your troubleshooting