Is there actually a dispute ('any difference') if the Contractor has not formally disputed the matter? Consequently, what would the Adjudicator actually decide upon?
Once a CE has been implemented (quotation is notified as accepted or notification of PM's assessment), the procedure has formally concluded under the contract. The main issue to consider is the principle of why the PM has made an assessment and whether the assessment reasonably allows for matters required to be included in a quotation (risk allowances, disruption, effect on other operations etc).
I appreciate that the right to refer a matter to adjudication 'at any time' may leave matters 'open ended'. Instead of adjudication, the Employer could consider a 'compliance assessment' whereby the PM's actions are reviewed by an independent third party to provide assurance, or otherwise, of the actions taken, notwithstanding any confidentiality issues.
Often, especially on a longer term, higher value project, a supplemental agreement or deed of variation is implemented to 'mop up' and conclude any outstanding issues to provide greater financial certainty going forward. This will obviously require some consideration, so the use will depend upon what the 'difference' actually is and the likelihood of matters being disputed.