Yes, you can do the ATP practical test in a Single Engine.
Have a read through Volume 5, Chapter 2, Section 14
Flight Standards Information System (FSIMS) It's a link to the online FAA Inspector's handbook formerly known as order 8900.1
I think the type ratings carry over but I am not sure.
You will need to call FAA Oklahoma and speak to somebody at "Airmen Certification & Licensing".
The number is here:
Flight Standards District Offices (FSDO)
Sidenote:
In order to take the ATP Practical test you DO NOT need an Instructor endorsement. Only should you fail you will need an instructor endorsement after additional training.
Let us know how things turn out,
Regards,