The 2.5/2.6 downgrader does indeed require GTA(the unpatched, older version).
The downgrader requirement that you were worried about was the need for a non-TA-082 motherboard. You can see if you have one by looking in the UMD slot at the top right corner of the motherboard, as shown here
0okm has been working on a downgrader for TA-082 motherboards with Firmware version 2.5, but I am unsure as to the safety or the progress of the program.
If your 2.5/2.6 psp does not have a TA-082 motherboard, you can safely downgrade using GTA or upgrade to 2.71 and downgrade without GTA.
2.71 downgrader thread
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