I had found many sellers selling replacement LCD’s for the PSP 3000, 3001, 3003 and 3004 models but when queried if they were suitable for the 3008 model all sellers responded had the same response. No.
I decided to give it a shot anyways as I thought the only difference between the 3xxx models was a number at the end to identify region.
So after installing a LCD sold as compatible with the 3003 model, I can confirm that Yes the LCD’s are compatible between the 300x models. It works flawlessly.