OK, so problem solved. I'll post the solution here just in case someone else is enough of a newbee to not know these things either.

I didn't have my device setting correct in Cool Edit. I was not getting or sending 32 bit audio as 3 byte Packed PCM. On the tracks’ recording panel, I was recording as 16 bit instead of 32 bit. (Changing this is the one that fixed the problem.)

Hope this helps someone else along the way!