My battery is finally starting to not hold a charge on my old PSP-1000 Phat. I do have a pandora, but I'm hesitant to mod that to a regular battery on the likelyhood I'll need to use it again (5 kids + myself with CFW PSPs in the house). I can only find batteries for the slims. First, will these work in my phat? If not, where can I buy a replacement battery for the phat?