When the escrow account for the delayed repairs was setup the amount put in the account was determined based on the estimates. When the account was established the rules for accessing the funds should have been defined.
I have seen these accounts where the item was cosmetic (as far as the bank was concerned) and it was very easy to access the funds. They could also be used as part of additional upgrades to the house. For example the carpet in the basement needed to be replaced, so the seller essentially set aside $x for the new carpet, but the buyer might contract for upgraded flooring and use a different vendor to save money and still get all the funds.
I have seen cases where the lender is involved in the process because they need to know the repair is made to protect their investment. They will want proof before the funds can be released.
You need to review the documents regarding what happens if the repair is more extensive than thought and the funds in escrow don't cover everything. Who is responsible for paying the contractor?
No matter what is in the documentation the scheduling of the repair will involve the buyer. The seller no longer has access to the property. Therefor timing and access issues can only be resolved by the buyer.