AngularJS validation using ng-messages without a form control

I store time as an integer of minutes in the database/model. However, I want to display it to the user in decimal hours (and let them edit the value using a number of buttons).

At the moment I have this:

<p class="input-group">
    <input type="text" readonly="readonly" value="{{vm.time.minutes|hoursMinutes}}" class="form-control" />
    <span class="input-group-btn">
        <ix-time-picker minutes="vm.time.minutes"></ix-time-picker>
    </span>
</p>

Of the 2 elements in the p tag:

1. The input type="text" works fine as the display mechanism. The hoursMinutes filter returns a formatted value, e.g. for 90 mins it will return '1 hour 30 mins'.
2. The ix-time-picker directive pops up a modal window with buttons such as 15 mins, 30 mins, 45 mins, 1 hour, 1:15 hours, etc.

This works fine - except for validation. I'm using ng-messages and I can't work out how to display the validation for the required state:

<li class="help-block has-error"
    ng-if="mainForm.$submitted"
    ng-messages="mainForm.minutes.$error">
    <span ng-message="required">
        Minutes is required.
    </span>
</li>

I don't have a control on the form called minutes (at least with an ng-model) so it won't display the message. I could add a hidden input with ng-model="vm.times.minutes" but as I need to use this repeatedly through the application, I'd prefer not to do that. Or at least I'd like to build some kind of common directive that merges the ability to have an ng-model on a control with the ability to display a value that is different to the model value, if that's possible.

Any suggestions?