I never used nor even own an HDD for PS2 before so i can't really help on that side but i transfer my Playstation 2 save files to my computer for almost 10 years now, and it did really help since i have so many games on that console, it was pretty mandatory for me to do so unless i wanted to delete thousand of hours of play. I transfer those save files with the help of an European action replay called the "Action Replay Max-2", that AR have an option called Memory Max that can let you transfer your save files from your Memory Card to a USB Drive and vice versa (it can only detect a small USB drive, small in data size i mean, i don't know the limit of the size it can detect but the one i use is 125 MB) and once they are on your USB drive you can easily transfer them to your computer, the memory card shown on my first picture below called Max Memory is not really mandatory since you can use any PS2 memory card with it but i put that as an
HUGE WARNING: that Memory Max option can not only corrupt your save files but can also corrupt your entire Memory Card, it's apparently pretty rare but it can happen, but in almost 10 years of use i never had any trouble with that Memory Max Memory Card, even though i tend to stay safe by copying the save files i can copy to another memory card before doing the transfer (that option can also format Memory Card so it can really be helpful if you stumble across a corrupt one during your hunts like i've found two of them a few years ago). It also doesn't care if those save files are copy protected or not, it let you copy them on your USB Drive anyway so save files from games like Monster Hunter or Timesplitters: Future Perfect are no trouble at all to move around.
The only negative point i have with that option is that those save files are unusable as they are on your computer since they are stocked as .max files and cannot be read by any PS2 emulator (i don't really mind since i prefer to use an actual PS2 to play but those who maybe wanted to continue their play on an emulator will have to search for another option).
That Action Replay is, like i already said, an European AR and i don't really know if any American (or any other European) Action Replay have that sort of option but if you have some Action Replay in your collection it doesn't hurt to check them (i had that MAX-2 for almost two years before i went to check all of it's options, i wanted to read an American DVD and the only DVD reader i had at that time was my PS2 so i started to check if any action replay i owned had that sort of option and if you are wondering yes it can also read DVD from any region, that is the third option on the second screen).
