Changing the property editor in v7 doesn't change any of the existing data, so you will still have int IDs in the database. Then the migration to v8 will just see that you're using the UDI-based property editor and expect that all the stored data is UDIs.

There are plans to support the legacy property editors in the migration and convert int IDs to UDIs, but that doesn't help you right now if you've already run the migration.

I think the easiest solution would be to add a custom version of MediaPickerValueConverter to your site, modifying it to handle both int and UDI values. I haven't tested it, but I think something like this should work:

public class IntFriendlyMediaPickerValueConverter : Umbraco.Web.PropertyEditors.ValueConverters.MediaPickerValueConverter
{
    public override object ConvertSourceToIntermediate(IPublishedElement owner, IPublishedPropertyType propertyType,
        object source, bool preview)
    {
        if (source == null) return null;

        var nodeIds = source.ToString()
            .Split(new[] { "," }, StringSplitOptions.RemoveEmptyEntries)
            .Select(id =>
            {
                if (Udi.TryParse(id, out var udi))
                {
                    return udi;
                }
                else if (Int32.TryParse(id, out var integer))
                {
                    var item = _publishedSnapshotAccessor.PublishedSnapshot.Media.GetById(integer);
                    if (item != null)
                        return new GuidUdi(Constants.UdiEntityType.Media, item.Key);
                }
                return null;                        
            })                
            .ToArray();
        return nodeIds;
    }
}

public class MyComposer : IUserComposer
{
    public void Compose(Composition composition)
    {
        composition.Register<IntFriendlyMediaPickerValueConverter>();
    }
}

That should solve any problems rendering templates.

You may still have problems editing the migrated content, but I think it should only be a problem if you have a multi-valued media picker and add a new item. Removing and re-adding the existing item before adding the new one should get around that.