Unfortunately, this is something that should be noted for anyone who cares about this speedrun. Here are the possible ways to play the game that I'm aware of:

• Disc in PS2 (several hardware variations, disc speed variations)
• Disc in backwards-compatible PS3
• Disc in XBox
• Disc in Gamecube
• Disc in backwards-compatible Wii
• Played off hard drive in fat PS2
• Played off hard drive in XBox
• Played off external hard drive on Wii
• Played off external hard drive on hacked Wii U?
• Played off microSD card through memory card port of PS2 via MC2SIO?
• Played through ethernet port on PS2 (others?) via something like RetroNAS?

I don't think I care enough to do much testing, but I just recently hacked my XBox and noticed the load times off that hard drive were significantly faster than I was used to with my PS2HDD (1-2s vs 4-5s). I had been using a microSD-to-IDE adapter with my PS2HDD and playing in widescreen which are two variables that can be changed to possibly improve PS2 loads. XBox doesn't seem to have widescreen mode and I was using a 2TB SATA HDD.

xbox loads for reference: