The contractor’s obligation is to achieve completion by the completion date, see clause 30.1. It cannot stop work while waiting for a compensation event quotation is agreed, see the last sentence of clause 61.1. If the contractor does stop work, the compensation event will be assessed as if they did not do so, see clause 63.7, which will put them in danger of breaching clause 30.1 and having delay damages levied.
The issue as to termination is dealt with in clauses 90 and 91. The employer can terminate if you have notified that the contractor has defaulted by substantially failing to comply with its obligations and not put that default right within 4 weeks of the notification, see clause 91.2 (R11). In summary the contract already deals with these issues and nothing further is needed.