sounds as if the present coating's in the ' chattahoochee ' style of overlay which is graded river aggregate embedded in mortar coating,,, its currently being reinvented under other names & includes water-bas'd epoxies,,, unsatisfactory stuff imo.
your contractor's right - in order to fix it properly, its all gotta come off,,, we'd suggest the same method,,, for that amt of work, we'd bill $4,840 + railing cost & it'd take about 4 days here in atl, ga,,, not a fan of acrylic bas'd mtls but, in the hands of an experienced artisan, they'll be satisfactory.
sorry - there's no silver bullet for this work,,, wood deck sounding better, lori ? ? ?