jay,
Charles and Scott have given you some good advice. I'll add my 2 cents.
First, removing deep swirls with a PC is not a sure thing. Especially on black paint. It's not that they can't necessarily be removed, but you may not want to remove the amount of clear coat required to get rid of them completely. However, as Scott said, you should be able to get the majority of them.
Now, I've also used a cutting pad on a PC with some success. Again, as Scott said, you may need to use a slightly less abrasive product after the 2.5 to remove any hazing.
Try the following:
Apply the 2.5 on the PC pad (cutting or polishing pad).
Put the PC lightly on the paint surface and spread the product around a 2' by 2' area.
Next, turn the PC on to say 3, and work that 2' x 2' area to make sure the product is spread evenly. (This also primes the pad well)
Now, turn the PC up to 5 or so (keep the pad on the paint & flat at all times) and work that area in various directions....... SLOWLY, SLOWLY....... did I mention SLOWLY.

A lot of people move the PC way to fast. You have to give the PC & pad some time to generate enough heat to break down the product (although 2.5 will break down pretty quickly).
When the 2.5 "starts" to disappear....... stop! (turn the PC off while the pad is still on the paint).
Wipe the area dry of any residue, and inspect. If you still see significant swirls, work the same area again in the same manner.
If you still see significant swirls after 2 passes with the 2.5, you may need more paint correction than you think. It could require a more abrasive product and the use of a rotary buffer.
If the area looks pretty good, you may want to step down to a lighter abrasive product and a polishing pad to remove any hazing and/or finish off the swirls. Again, if you've used a "cutting" pad, chances are you will have to step down. If you've used a polishing pad and been successful removing the swirls, you might able to go directly to a glaze or your LSP.
As for the Zaino Z2 (or Z5), you can apply it with a finishing pad, but it's also very easy to apply by hand. If you get the "knack" of applying it with a PC, you can apply very thin coats.
Of course, the above works for me. I'm sure others have equally good processes.
Hope this helps.