Thanks Dan for all your ideas and suggestions here. Also, indeed it does sound sort of like a microphonic tube in a way! Interesting, no?
Not to jump to conclusions, but I think I've determined what may be the problem.
As an independent IT consultant and hobbyist Hammond Organ fixer by a few nights a month,

I've found the issue I've been having with the Oasys most intriguing since the keyboard combines beautifully written software with awesome hardware. From all I could look at and determine, it looks like all the sound generation and effects occurs in the computer, in software, and the handling of inputs and outputs and controls is handled through proprietary hardware.
I began to look at this more like a computer software problem, and as I often do with computers that have random crashes in the field, I popped a copy of MemTest86+ in the CD drive, plugged a USB keyboard in, and started it up. When I woke up seven hours later, this is what greeted me:
For those of you who may be unfamiliar with MemTest86+, yeah, all that red stuff, that's bad.
So, I'm going to put some of this on order
http://www.newegg.com/Product/Product.a ... -_-Product and as a bonus I'll finally be getting that 2GB that you need to use ESx1 and ESx2 simultaneously.
Also, my god this thing has a fan in it. As soon as MemTest started it kicked the fan to high. I woke up last night and instinctively went to go put my PowerMac G4 back to sleep before I realized I sold it two years ago and the Korg was still making all that noise.
Also, at the completion of the test, the Boot CD sent the ACPI off event, turning the computer off even though the power switch was on. Since there's no soft power button on the Oasys, this was a fun one to figure out.
Anyway, I'm pretty happy that I think it's nailed down to being a simple fix. I'll let everyone know what happens.
Edit: Indeed, Akos, the "Bell Bell & Bell" patch is a beautiful one.
