Legally, it is the for the executor to decide how to proceed, and the executor is constrained by the instructions given in the will. The fact that 5 beneficiaries are of one view, and 3 have a different opinion is not relevant (except in the matter of family relationships, but I suspect that they are already damaged).
I think the wording of the will is critical, and your sister should get the advice of a solicitor on how it is to be interpreted. I suspect that if she offers within four months to pay the discounted price, she might be okay -- but that her offer would need to be unconditional. It might then take some time (a number of months) to complete the sale to her.
What your sister might need to do is find a bank willing to provide bridging finance (not easy in today's environment, but not impossible) and she might find herself having to sell her house in a hurry, taking a risk on the price it realises.
The executor should not have any role in deciding who her selling agent should be.