Luc,
I've found HM's extended warranty plan to be a complete waste of time and money, they will find any excuse not to honour it, they changed uder warranty a heat exchanger on my 427 which had failed then told me 2 months after it was frost damaged and sent me a bill for it, that's after the 808 mile round trip and the 2 days lost earnings, costing just over £1600. The failure happened on the 21st May(frost damage - I don't think so)
Yours clearly has an engine problem so get it to a Briggs main agent, the guarantee is for 2 years and they stand by it.
Get it sorted and learn from my experience