To apply for the CPL license itself you have to have the requirements you mentioned. You no longer need to do a 170A but a lot of schools still do them, probably a nice way to make some money but it's also nice to do a practice test with a different person.
You need 200 hours to apply for the license, but only 150 (100pic) to start CPL training.
Also bare in mind that you have 3 years to complete your IR after your last ATPL exam or your exams expire and you have to do them again. You also have 7 years to get your ATPL unfrozen or you have to do the exams again.
Personally, I would stick to one modular school as I've seen some airlines require all training at one school.