Hi Eric,
One possible solution is to use a string attribute to send the datetime via Rest.
In other words opt not to send the datetime attribute in your export mapping and instead create a string attribute on the same entity and use that in the export mapping. To populate the string just parse the datetime using the method you described above, simply don’t convert back to a datetime.
When the attributes are converted to JSON they are essentially all treated as string values anyway, so as long as the format that you parse the DateTime with is compatible with your REST service consumers, it shouldn’t be any different on their end.
Hope this helps,
Danny Kumpf