well first i just have to point out the bad luck you have lol
If you had 2.71 you could have just downgraded to 1.50 then installed CFW from there But sadly with 2.82 your stuck with HEN or getting stuff like GTA or Pandora's battery.
1. I would just buy a pandora's battery for like 6$
http://www.dealextreme.com/details.dx/sku.12472~r.24128850I have had this battery now for a good 2 years and still going strong.
2. If not that then try the chicken HEN or ChickHEN hack (not sure how it's spelled)
I am not really up-to-date on how it's done But know it's easy But not sure if PSP Fats will work with it, as i tried the hack myself Back in the time when it first came out and did not work on my PSP Fat.
3. Buy a Unpatched version of GTA then update to 3.03 and use the downgrader to go to 1.50 then install cfw from there.
Still your Best bet is the pandora's battery as it's SUPER cheep and easy to use, and as a Plus you can unbrick any PSP (well any psp version under TA-088v3 LOL)
ps.. Sorry it took me so long to reply back, I was watching a movie