Using @XmlEnum to generate an enum of type Integer in json schema

I have the following Java enum:

@XmlType
@XmlEnum(Integer.class)
public enum DefaultMessageVersion
{
@XmlEnumValue("1") ONE;
}

That is producing the following json schema snippet:

"defaultMessageVersion" : {
"type" : "string",
"enum" : [ "1" ]
}

This is because (I believe) Jackson ignores the @XmlEnum annotation. I would like the outputted snippet to have "type" : "integer" (or int? I'm not 100% sure which it is). I'm going to attempt to write the functionality myself, but would appreciate any pointers on where to get started, or a head-up if I'm just wrong about why it's not working.