Good plan on getting mortgage fully sorted and clear asap. And ok, but what are they offering in exchange for that? Money off asking price or some allowance from the final sale price?
You should be getting a fair whack off if they expect you to wait for 6 months. They should be happy to be getting it all sorted too rather than remarket. Has this been discussed? I would push hard for sure. But sounds good that exchanging looks realistic soon. Did you have a survey.. no issues? Nothing to ask for money knocked off there?
You're assuming that Thora ie purchaser holds the cards here, but in reality, for the reasons Thora has already explained, it's the vendor who holds the cards.
There's no incentive for the vendor to give Thora a discount in recompense for Thora and her family being strung along and waiting for a 'how long is a piece of string' completion and moving in date, because the market is moving so fast.
As Thora's already explained, if she tries to play hard ball and insist on setting a completion date, or else they withdraw their offer and walk, the vendor is simply going to call their bluff and say 'walk, then', because they know they can put their house back on the market and sell it for an even higher price within a week, possibly even 24 hours.
And the vendor knows that Thora's got more to lose in this scenario, having forked out for surveyors and a certain amount of legal fees to date.
And the vendor also knows that if they exchange, the cards in their hand become even stronger, because then they can take their sweet time till completion (what if the property developer of their new build goes bust because of increasing cost of materials/labour?) safe in the knowledge that they have Thora's deposit, and if Thora gets fed up of waiting and wants/needs to buy somewhere else, then she will forfeit the deposit on top of writing-off the cost of survey and legal fees to date.
Thora simply doesn't have the negotiating power you think she does in this scenario, sadly.