For homebrew enthusiasts with TA-082 or newer motherboards, who have a patched idstorage key and cannot upgrade their 3.11 firmware to 3.50 to use the 3.50 downgrader, and don't have access to Pandora's Battery, team N00bz has a solution for your extremely specific problem.
Their new 3.11 downgrader will let you go down to firmware 1.50, at which point you could then do lots of homebrew goodness. You will need a copy of Lumines to pull off the downgrade. Detailed instructions can be found here. As usual, we must warn you that there is a risk of bricking your PSP, so use at your own risk.