By default the format of the date component is incorrecnt and will need to be converted to uppercase to work with moment.js. You could do something like this which should work.

var dateFormat = g_user_date_format.toUpperCase();
// get the full date time format
var dateTimeFormat =g_user_date_time_format;
// construct correct date time format where we strip the date and use the upcase version
var newDateTimeFormat = dateFormat + dateTimeFormat.substring(dateFormat.length);

//create date object using moments and correct date time format
var dateObj = moment(g_form.getValue(‘the_date_field’), newDateTimeFormat);

Unfortunately, I haven’t found a great solution for Service Portal yet. I think it’d be a great enhancement request to ServiceNow to add support back in. If I can find something I’ll post it here.