Just to elaborate some more, I was helping
@hoodangel troubleshoot Tekken 6.0 using GEX OFW 4.70 on my Namco System 357C. I have confirmed before that the game works fine on firmwares 2.51,3.60, and 3.70 as the HDD we got is a special firmware free HDD. I did a few tests before with GEX OFW 4.XX but for the games I play, I don't need newer FW, most games from the launch of the system to around the early 2010s can run on 3.60/3.70 GEX OFW perfectly fine. Taiko no Tatsujin games being the exception which used 4.XX GEX FW when the series first appeared on the platform.
I'm not no where near an expert at how these systems/games work but this is from some research I've gathered from the past two years.
Tekken 6.0 originally shipped with 1.90 GEX FW and T6BR shipped with 2.51 GEX FW and those also seem to have been locked to a specific firmware version at first but some special firmware free game HDDs also exist. These versions allow you to use any firmware and some, mainly the Japanese versions of those HDDs have a newer PS3UPDAT.PUP file inside the ARCDIR folder, the firmware file can be either 3.60 GEX or 3.70 GEX OFW. I also own some export versions of these special "3.40" HDDs (for T6BR) and these don't have the .PUP file. You can also install newer FW and the game should actually still work. I actually had to do this so T6.0 could work with 4.70 GEX FW or else if I did it the other way around (use 4.70 FW on a HDD and install the game that way), the game would constantly bootloop, so I had to install 3.60/3.70 then I can update to newer 4.XX FW. The later games released on the system don't have this weird issue with FWs unless it requires a specific firmware version to boot into the game.
Take this with a grain of salt as again, this is all theoretical, I don't have a clear understanding on how these systems/software really work.

Below I have posted a picture of some T6BR HDDs I have in my collection, if you have any questions, feel free to ask away
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