An acceptance of the trades or of the entire contract plays absolutely no role in the creation of additional costs and in my opinion has no influence at all on the enforcement of higher costs. The question is whether exceeding the deadline of the flat rate price can automatically lead to an arbitrary readjustment of the price? [...] One must be allowed to assume that the price was cost-covering for the general contractor until day X. From day X onwards, no longer. Accordingly, he has to break down the costs.
That the OP is mistaken in considering the achieved construction status as "checked off" is already significant. However, I agree with you that the general contractor should nevertheless treat this, let’s say, "past" as a fictitious "reading date" if one wants to act properly by mutual agreement. Legally, there will rather be a clear assignment of roles as to who the loser is here: namely the one who was more negligent during the drafting of the contract. At least one of the contracting parties probably thought too little about what should apply if the work is not completed within the planned time. If the contractor did not take into account his risk of underestimating cost increases here, then one will have to look to the law as a fallback (here: Building Code). The gap in the contract is of course more favorable to both sides to be settled by voluntary agreement. The law can certainly also be applied without a judge’s ruling ;-)
So, generally, if I buy a house and the contract states a fixed price with the associated services that have to be provided for this price, then as a buyer I would assume that the materials for this house are already paid for and in stock at that point in time.
At least you may assume that price increases are not your problem. Based on the little we know here about the individual case, my assessment is that both sides were probably negligent when drafting the contract. Accordingly, I would suspect a court ruling close to the "mediation result," voluntarily applying the law.