You can use this downgrader on your 2.71 PSP, you just need to follow step 1 and upgrade to 3.03 before you downgrade.
You cannot install the custom firmware without first downgrading to 1.5 (unless you already have a previous version of the custom firmware installed).
Edit: Do what evolve posted, doesn't need the copy of GTA.
Sorry, was rather drunk when I posted this and didn't think of the 2.71 downgrader

Cheers Evolve.