If you can burn CD's on another computer, you could burn the files and installers you need to a CD in the boot sector. You might need to create several CDs, though (I do this a lot).
You can make a CD to install DOS 6.22 to start. There are a number of ISOs out there for DOS. You could use a program like UltraISO to modify the ISO to include your sound card's drivers in a separate folder so you can set up the sound card's CD driver. Then burn the installation disk.
Next, you'll need to burn a CD just for the drive overlay software. I use UltraISO to create a new CD image, and I simply put the Ontrack floppy image into the boot sector and burn the disk. It's a little wasteful, but I've got tons of CD-Rs to use up.
Use the drive overlay CD to boot a donor computer via CD into the drive overlay software to prep a large hard drive (your 2.4GB would do). Tell Ontrack that you have the BIOS set to a 512MB HD (it really doesn't matter if the donor computer can handle more than that). Then use the DOS CD to install the OS through the drive overlay. Finally, install the sound card's drivers. Then put the hard drive into the Gateway. Make sure to set the Gateway BIOS to a 512MB drive.
Once you have Ontrack working, you can use it to boot from CD into another OS. Just be aware that this won't work on a cold boot because the IDE interface on a sound card won't have pre-initialized. You need to boot into DOS (or some other OS) first and run the IDE interface driver to initialize the card. Once initialized, you can Ctrl-Alt-Del to restart the computer, and Ontrack can boot from the CD. Pretty handy.