ATP
You can do the ATP during recurrent. You will have to let the training provider know that you will do so. So you will do a recurrent/upgrade instead of just a recurrent. Depending on the training provider you may or may not have to do an extra day. The notice is to allow the provider to assign the properly authorized instructors/evaluators to your training events. It sounds a little strange that the training provider would not do a full type rating because you didn't have the ATP written. I have seen private pilots with full type ratings. Could it be a requirements of your employer?