Here is a systematic review with a focus on extracorporeal removal. From the review:
The workgroup concluded that carbamazepine is moderately dialyzable and made the following recommendations: ECTR is suggested in severe carbamazepine poisoning (2D). ECTR is recommended if multiple seizures occur and are refractory to treatment (1D), or if life-threatening dysrhythmias occur (1D). ECTR is suggested if prolonged coma or respiratory depression requiring mechanical ventilation are present (2D) or if significant toxicity persists, particularly when carbamazepine concentrations rise or remain elevated, despite using multiple-dose activated charcoal (MDAC) and supportive measures (2D). ECTR should be continued until clinical improvement is apparent (1D) or the serum carbamazepine concentration is below 10 mg/L (42 the μ in μmol/L looks weird.) (2D). Intermittent hemodialysis is the preferred ECTR (1D), but both intermittent hemoperfusion (1D) or continuous renal replacement therapies (3D) are alternatives if hemodialysis is not available. MDAC therapy should be continued during ECTR (1D). Conclusion. Despite the low quality of the available clinical evidence and the high protein binding capacity of carbamazepine, the workgroup suggested extracorporeal removal in cases of severe carbamazepine poisoning.