Nested populate match query - mongodb

Question

Here is an example of the data I am working with:
// group
{
name: 'Group 1',
phases: [ {name: 'Period 1', startDate: "some date", endDate: "someDate", schedules: [{startTime: '1:00', endTime: '2:00', schedule: 'mongoIdRef'}]}, { name: 'Period 2', startDate: "some date", endDate: "someDate", schedules: []}, { name: 'Period 3', startDate: "some date", endDate: "someDate", schedules: []}, { name: 'Period 4', startDate: "some date", endDate: "someDate", schedules: [] } ]
}
// schedule
{
condition: 'active',
tz: 'US/Mountain',
daysOfWeek: [{startTime: 9, endTime: 22, days: [2,3,4,5]}, {startTime: 2, endTime: 5, days: [2,5,6]}]
}
The group's nested "schedule" property needs to get populated. I am doing this successfully here:
Group.statics.findForDate = function (date) {
date = moment(date);
return this.findForDate({
phases: {
$elemMatch: {
startDate: {$lte: date},
endDate: {$gte: date }
}
}
}).populate( {
{
path: 'phases.schedules.schedule',
match: {'daysOfWeek': { $elemMatch: {days: date.day() } } }
}
})
}
However, the match doesn't match properly. I want to return only groups that have a schedule that has the date.day() (which is a number 0-6) in the days array. How can I get .match to do this? Is there another approach?