We cannot comment on your contract management system but confirm there is no ambiguity in ECC with regard to withholding of acceptances.
First, clause 13.4 requires you to give your reasons for withholding acceptance of a communication submitted by the contractor for acceptance. This clause does not limit what reasons you can give for that withholding, and nor does any other clause in the contract. Therefore, you are entitled to give any reasons you want for withholding acceptance of a communication issued for acceptance, as long as a reason is given.
Second, clause 13.8 makes it clear that withholding acceptance for a reason stated in the contract is not a compensation event. Third, as you say, clause 60.1(9) makes it clear that withholding acceptance for a reason not contained in the contract will be a compensation event.
You are therefore able to give any reason for withholding acceptance of a programme issued by the contractor for acceptance and you are not limited to the reasons set out in clause 31.3. If the reason given falls within those in clause 31.3, that withholding will not be a compensation event; if the reason falls outside those in clause 31.3, it will be a compensation event. Given that position, it seems essential that any contract management system you are using should allow for a category that falls outside the reasons given in clause 31.3, or any other similar clause, otherwise it would not comply with the requirements of the contract.