After digging through the media modal code, I came up with the answer to my question:
wp.media.controller.Custom = wp.media.controller.State.extend({
initialize: function(){
this.props = new Backbone.Model();
},
// called when the toolbar button is clicked
customAction: function( controller ){
// get the value of a media view template form field using
// this.props.get('key'), where 'key' is the value of its
// 'data-setting' attribute
console.log('width: ' + this.props.get('width'));
console.log('height: ' + this.props.get('height'));
}
});