I still read 61.5 as being applicable. If a Contractor waits 2 weeks before raising an early warning, the Project Manager can still use clause 61.5 to say that they ”did not raise an early warning of an event that an experienced Contractor could have given”. The fact that they have just given one does not mean that they can not be held to account for not raising it 2 weeks ago. The intent of this clause and that of 63.5 is for the chance for the Project Manager to mitigate the problem to lessen the time/cost impact to the Employer. The fact that the Contractor has finally gotten round to raising the issue does not mean that they should not be held to account for not raising it before now.
Otherwise this could lead to a (risky) game of the Contractor holding onto an early warning until just before they think they have been found out and then raising it before the Project Manager does. Clearly this would not be the intent of the contract. With this in mind I believe this clause is applicable if they have not raised an early warning at all or if they did not raise it early enough where you can prove (may be difficult) that they did know about it.
Your last point about waiting to raise an early warning until just before the end of the 8 week period raises a far different question. The 8 weeks should be irrelevant, as it has to be something you are aware of if the 8 week time bar is to be applicable, and if you know about it I would suggest it is no longer an early warning (as early warnings are for matters that could or might be an issue). Last line of 16.1 states that an early warning for a matter already notified as a compensation event is not required.