The 142 schools will just have another class for the ACTP certification before you take the written. The class is 24 classroom and 16 sim hours so say 8-10 days. Then you go take the written and then you start the class you came for.
The 2 years airline experience requirement is only for the instructors teaching the ACTP class. AllATPs can still have 300 hour CFIs providing flight training in light twins but the student will have to have their ACTP paperwork when they show up.