How to use reflection to link a const string field from one class to a readonly object field in another class

I have a class containing string constants and a class containing readonly objects representing a counter object. I have created a custom attribute that tags the string constant with the string representation of it's corresponding counter. Is there a good way to link the string const to the counter object using the attribute?

Here is an example of the string const:

public static class OperatorDiagnosticsConstants
{
  [CounterType(CounterType = "ReagentProbe1")]
  public const string R1_PROBE_CODE = "SACT-158";
}

Here is the class containing the readonly counter objects:

public class MaintenanceCounterType : CounterTypeEnum
{
    public static readonly MaintenanceCounterType ReagentProbe1 = new MaintenanceCounterType(MaintenanceCounterTypeConstants.ReagentProbe1ID);
}

I can think of two solutions but wonder if there is a more elegant way? First is in the code that uses these two classes, I could have a convert method with a switch statement. Switch on the attribute string to return the MaintenanceCounterType

public MaintenanceCounterType Convert(string attributeStr)
{
   switch (attributeStr)
   {
      case "ReagentProbe1":
        return MaintenanceCounterType.ReagentProbe1;
      ......
   }
  }

Or I think I could add the same custom attribute CounterType to the MaintenanceCounterType and use reflection to match them up. I guess by checking the equality of the string property of the custom attribute?

Looking for a more elegant solution. Thanks!