I was able to get this working with the custom EditorDescriptor described above, along with a custom Dojo widget that inherits from the relevant built-in widgets and overrides the "uiType" property for the "GroupName" meatadata.  I'm not sure if this is the best way to accomplish this, but it seems to function as desired. See below for details.

EditorDescriptor

[EditorDescriptorRegistration(TargetType = typeof(ItemCollection<CommerceMedia>), EditorDescriptorBehavior = EditorDescriptorBehavior.OverrideDefault, UIHint = Constants.UIHints.CommerceMediaCollection)]
    public class CommerceMediaCollectionEditorDescriptor : EPiServer.Commerce.Shell.UIDescriptors.EditorDescriptors.CommerceMediaCollectionEditorDescriptor
    {

        #region Constructors

        public CommerceMediaCollectionEditorDescriptor(LocalizationService localizationService, AssetUrlConventions assetUrlConventions) : base(localizationService, assetUrlConventions)
        {
            
        }

        #endregion

        #region Public Methods

        public override void ModifyMetadata(ExtendedMetadata metadata, IEnumerable<Attribute> attributes)
        {
            ClientEditingClass = "editors/CommerceMediaCollectionEditor/Editor";

            var assetGroupNames = typeof(Constants.AssetGroupNames).GetConstantValues<string>().Select(x => new {
                text = x,
                value = x
            });

            metadata.AdditionalValues.Add("assetGroupNames", assetGroupNames);

            base.ModifyMetadata(metadata, attributes);
        }

        #endregion

    }

Dojo Widget

define([

    //dojo
    "dojo/_base/declare",
    "dojo/_base/array",
    "dojo/_base/lang",
    "dojo/when",

    //epi
    "epi-ecf-ui/contentediting/editors/CommerceMediaCollectionEditor"

],

function (

    //dojo
    declare,
    array,
    lang,
    when,

    //epi
    CommerceMediaCollectionEditor

) {
    return declare("site.editors.CommerceMediaCollectionEditor", [CommerceMediaCollectionEditor], {

        //overrides
        postCreate: function () {

            this.inherited(arguments);

            //after the model is initialized, override the the UI for the GroupName property
            when(this.model.initialize(), lang.hitch(this, function () {
                this._initGroupNamePropertyEditor();
            }));

        },

        //private methods
        _initGroupNamePropertyEditor: function () {

            //get the group name property from itemMetadata
            var groupNameProperty = array.filter(this.model.itemMetadata.properties, function (property) {
                return property.name == "GroupName";
            })[0];

            //use built-in epi SelectionEditor to render dropdown
            groupNameProperty.uiType = "epi-cms/contentediting/editors/SelectionEditor";
            groupNameProperty.selections = this.metadata.additionalValues.assetGroupNames;

            //set initial value to first dropdown element (the "initialValue" property is defined/implemented by base CollectionEditor, and is then passed to SelectionEditor as the value property)
            groupNameProperty.initialValue = groupNameProperty.selections[0].value;

        }

    });
});