I've got it to work using an override method.

Basically, the displayValue is what I wanted to display ('Standard') and the value is what I wanted to execute (value: 1). Apparently, the remote store is a little tricky to work with, so that's why the override was necessary.

        var hatComboStore = new Ext.data.JsonStore({
                autoLoad: true,
                fields: [
                    'BIN_ID',
                    'BIN_DESC'
                ],
                baseParams: {
                    method: 'post'
                },
                url: 'json_bin_hat.php'
        });

        var hatCombo = new Ext.form.ComboBox({
            allowBlank: false,
            autoSelect: true,
            displayField: 'BIN_DESC',
            displayValue: 'Standard',
            emptyText: 'Select a hat...',
            fieldLabel: 'Hat',
            forceSelection: false,
            hiddenName: 'hatId',
            itemId: 'hatId',
            listEmptyText: 'No records found',
            listeners: {
                afterrender: function(combo, record, index) {
                    var hat = combo.getValue();
                    binCombo.store.baseParams.hat = hat;
                },      
                select: function(combo, record, index) {
                    var hat = combo.getValue();
                    binCombo.store.baseParams.hat = hat;
                },
                focus: function(combo) {
                    binCombo.clearValue();
                }
            },
            mode: 'remote',
            msgTarget: 'side',
            name: 'hatDesc',
            store: hatComboStore,
            submitValue: true,
            triggerAction: 'all',
            valueField: 'BIN_ID'
            value: 1
        });

        //Override method to default hatCombo value to 'Standard' while underlying value = 1
        Ext.override(Ext.form.ComboBox, {
            initValue: Ext.form.ComboBox.prototype.initValue.createSequence(function() {
                if (this.mode == 'remote' && !!this.valueField && this.valueField != this.displayField && this.displayValue) {
                    if (this.forceSelection) {
                        this.lastSelectionText = this.displayValue;
                    }    
                    this.setRawValue(this.displayValue);
                }    
            })
        });

Looks like the value prop is not working for remote stores. Probably the combo is rendered before the store has loaded. You can set the value after the store has loaded.

This works for me (tested as an ExtJS 3.4 fiddle).

var hatComboStore = new Ext.data.JsonStore({
    autoLoad: true,
    fields: [
        'id',
        'title'
    ],
    url: 'https://jsonplaceholder.typicode.com/todos'
});

var hatCombo = new Ext.form.ComboBox({
    fieldLabel: 'Hat',
    store: hatComboStore,
    displayField: 'title',
    valueField: 'id',
    mode: 'local',
    submitValue: true,
    triggerAction: 'all',
    // Apparently does not work with remote store.
    // value: '1'
});

hatComboStore.on('load', () => hatCombo.setValue('1'));

new Ext.form.FormPanel({
    items: hatCombo,
    renderTo: Ext.getBody()
});

see example of setting default value:

Combo config:

{
    triggerAction: 'all',
    id: 'dir_id',
    fieldLabel: 'Direction',
    queryMode: 'local',
    editable: false,
    xtype: 'combo',
    store : dirValuesStore,
    displayField:'name',
    valueField:'id',
    value: 'all',
    width: 250,
    forceSelection:true
}

source: Extjs 4 combobox default value