Your european ATPL written will not suffice. You will need to take the FAA written.
You do not need to do this with Simuflite or FSI...you can do it at any flight school in the US that has testing facilities. The cost will be eighty to one hundred US dollars...somewhere in that range, depending on where you go.
You do not need a course. You can buy the preparation software for a few dollars and study on your own.
You can take the practical ATPL test at the same time as the type rating test. Functionally, the type test and the ATP practical exam are identical; same maneuvers, same procedures, everyting. It's the same ride. If your paperwork is prepared in advance, there's no good reason why you would need to take the type ride, then go back for the ATP ride.
Let your training provider know in advance what you intend to do.