HR34 RB20DE Neo - engine shakes as if there is a missfire

Hi, I have an RB20 Neo Skyline R34. Only 85K km. Actually it's my son's first car but I'm troubleshooting it. We bought it, checked oil and on the dipstick it looked like brand new - very light, not dark dirty oil so we figured out we would change it later. Started looking for an oil filter in no rush, got an original one from Pitworks and during that time in about two months son put about 1000km on it and then started having issues. It started fine, you start driving it and the steering wheel felt vibrating or shaking. I immediately thought that maybe one of the tires got a buldge on it from being old, by that time I already had new front tires so got back tires checked and was told there was something wrong with them - story short - got new tires. Then I drove it myself and when I stopped - i felt that vibration shaking when I'm not even driving it. Opened the hood, felt the engine and it could feel it kind of jerking/shaking at times as if there is a missfire. Immediately i changed oil and it was super dirty. Also changed all the sparkplugs - didn't help. This doesn't start right away when you start the car but you let it run for a couple minutes and then it starts happening. The hotter it gets the more you feel it.
I thought it might be a coil - tried testing resistance and it was the same. Bought two brand new oem coils and tried changing first two, then the next two and then the last two and made no difference. Then I thought what if there are two bad coils like 1st and 5th or 6th and by changing them by two I still might have had one faulty one, so I bought four more oem coils and by this time I had all six coils brand new - didn't help. Then I cleaned injectors - that's turned out a waste of money - cost $400 but didn't fix the problem. Needless to say I also changed fuel filter too. Then I bought a new MAF and tried that. Then I bought a new rear cam sensor that's at the bottom closer to the transmission and that made no difference. Then I bought a front angle/cam sensor, not new, it was used but working - made no difference. Then got an ECU from another RB20DE Neo and tried that and that didn't help. Then I cleaned the idle air control valve, that didn't help, solenoid on it was humming so I bought the whole idle air control valve and replaced it. That didn't help either. Then I had two more things to try - there is a small valve stuff - SOLENOID VALVE ASSEMBLY Genuine Nissan (1495638U0A) - I got that brand new and replaced it - still the issue is there. There is another valve stuff right next to it - (Nissan 14930-AA00A - VALVE ASSEMBLY-CONTROL) - that's the last one that's i'm going to replace but I'm still waiting for this to arrive and if it doesn't fix it - i'm out of ideas. I don't think old dirty oil and late oil change would have been the cause as when it runs cold - it is not shaking and that starts only after it warms up. Now the weather is getting hotter and I can see it now shaking almost right away after starting but if this was an engine damage due to bad lubrication - I would assume I would feel it right away when you start the car, not when the engine warms up. it really does feel as if one cylinder missfires and I can't locate it to any particular cylinder.
Any ideas what to try would be super appreciated.