5mm is not a lot of gap. You want to be closer to a full cm. I'm still thinking that a new HT coil is in order.
Assuming your spark is fine, the only other reason for a wet plug with no firing is flooding, like you said. However, the carb is designed to overflow out of the top of the carb, and it would be hard to flood the cylinder even if you had a bad float needle. So too large a jet would explain that, but it seems to me to be an unlikely scenario.
The fact that the bike runs and dies also points to a bad HT coil. When the coil warms up it performs worse, classic HT coil issue.
New one on Amazon is 15 bucks. Emgo universal coil is a perfect fit.
You might consider making some videos of your symptoms. Show us the spark. Show us how it runs and then dies. Pics of your parts also. That would make it easier to help you.