Misfire code in cylinder #6 after head gasket replacement but it's not a misfire? Ford mustang GT 2002?

So I just did my head Gasket in my 02 GT 2V but afterwards it ran great no hesitation in driving idles great. But I'm getting a code for p0306 and another code p0316 (misfire found within first 1000 rotations) the car itself doesn't have any skips or chugs when idling or whilst driving.

Here's the other thing the code only comes up when the motor is hot, if it turn it off and restart it when it's up to operating temperature it sets the code. When it's cold there's no code. I've driven from cold start to all the way warm 30+ min no code. As soon as I turn it off and restart solid code. Another odd thing is it's not flashing like I've seen misfires do as well it stays solid on the dash. I do know the exhaust had quite a bit of water from a blown head gasket could that cause a catalytic converter to go out?

I've read that sometimes this is an issue. And before we ask "have you checked for spark, fuel, compression?" Yes all three check out just fine. They are operating normally. In fact I checked all cylinders for all three.

A bad catalytic converter WILL NOT cause one cylinder to misfire. The computer is MUCH more capable of determining a misfire than you are. Most likely the spark plug is bad. Switch plugs between two cylinders. Check your spark plug wires. Re-seat the one on both ends to the spark plug. Then check the compression. If all else fails, you may want to swap two injectors.

Now a head gasket blows from overheat and pressure, you said its overheating, that means you didn't fix the head gasket problem you just replaced it, your going to blow it again. Your coolant is not reaching the engine, the thermostat says its fine, cause its not in the engine so the dash temp guage is not going to be in the red, but your misfiring cause its to hot. To put it simply, your running your car with NO coolant (but you do have coolant, its not cooling your engine though, thats probably why the head gasket blew in the first place. Something is blocking your engine from allowing coolant to flow though. No coolant to cool engine, bye bye new head gasket again.

Get your car nice and hot(not scalding hot) just normal operating temp, your coolant hoses will get warm. Now follow the hoses to the engine bay where it enters and see if the hose feels hot or cold. If hot its going in, if cold wait 10mins, and feel again to see if the engine opens up, if still hot good, if cold still thats where the problem is, do this to each side and every single tube coolant is hot you will know, you might have also flooded the engine with water when the gasket busted, thats where the water is coming from not from the cat converter. If it drips water very slightly, it's not to bad, but if its dripping alot like contant flow it's not combusting correctly (water is normal when first starting the car and warming it up)