Kizashi Club

I dont have any experience with running 2 different fuels. I would try cleaning throttle body and maf erasing codes, disconnect battery for 30 sec then drive for a week on petrol and then check data long fuel trim and check for trouble codes on engine. The vvt actuator sticking is the usual issue but throws a correlation code along with rough running at idle that doesnt go away so quickly. On yours if I was to guess, maybe injectors.

two things
1- Kizashi does not have an EGR system.
2- vacuum leak makes your engine RPM goes up not down.

also, is your engine air filter clean? you didn't mention changing it.

I suspect it to be related to LPG fuel. When driving in LPG mode, turning off the engine leaves LPG (gas) in the engine (just my thoughts). So when next time starting the engine, it has to get rid of this gas, then pump and pressurize new petrol, then create air-petrol mixture to be able to ignite, which 1) takes some time, 2) requires ECU to recalculate timings because it was set to LPG mode before? Or am I completely wrong?

I have the same problem like you described and the core of the problem are the valves (diagnostic error shows "misfire" on cylinder 4).
My Kizashi is also LNG+Gassoline and it will affect the valves.
Solution is to replace these parts (see image):

Image link : https://ibb.co/WKPXw5R

The problem was with liquid gas to vapor converter, reducer or what's the name. Car has this LPG addon so that it can drive on LPG fuel. The reducer requires maintenance from time to time, and after re-sealing it the issue was gone.